Intersection Form Research Articles

Examples of topologically unknotted tori

We show that certain smooth tori with group Z \mathbb {Z} in S 4 S^4 have exteriors with standard equivariant intersection forms, and so are topologically unknotted. These include the turned 1-twist-spun tori in the 4-sphere constructed by Boyle, the union of the genus one Seifert surface of Cochran and Davis that has no slice derivative with a ribbon disc, and tori with precisely four critical points whose middle level set is a 2-component link with vanishing Alexander polynomial. This gives evidence towards the conjecture that all Z \mathbb {Z} -surfaces in S 4 S^4 are topologically unknotted, which is open for genus one and two. It is unclear whether these tori are smoothly unknotted, except for tori with four critical points whose middle level set is a split link. The double cover of S 4 S^4 branched along any of these surfaces is a potentially exotic copy of S 2 × S 2 S^2 \times S^2 , and, in the case of turned twisted tori, we show they cannot be distinguished from S 2 × S 2 S^2 \times S^2 using Seiberg–Witten invariants.

Comparing the South African and Brazilian student uprisings (2015–2016): Similarities, Circulations, and Distance

ABSTRACT South Africa and Brazil are notorious for having some of the highest levels of (racialised) inequality on the planet, and dysfunctional education systems failing millions in their aspirations for a better life. Over 2015-16, student protests erupted across Brazilian and South African schools and universities, challenging these conditions through strikes, occupations, on-campus and street protests, and intellectual production. This paper builds on a World-Systems theoretical framework to understand the similarities, circulation, and distance between the two contemporaneous movements. In Brazil, the ‘Primavera Secundarista' high school occupations dealt primarily with local political dynamics, such as school closures, and intersectional forms of oppression. In South Africa, the ‘Fallist' university mobilisations demanded free, decolonised education, alongside addressing issues of outsourcing and institutional racism. In the first section, I give a comparative overview of these student movements’ similarities, situating them in their context and highlighting the key concerns and political and pedagogical practices of student activists in each. While these movements did not generally engage with each other, there were some important points of interaction, discussed in the second section. While highlighting these points of connection, I also advance an argument in the third section for why there was nevertheless relatively little direct engagement between these contemporaneous movements that otherwise had so much in common. The points of connection and disconnection between these similar movements offers insights about the functioning of the contemporary World-System and the modes of transnational circulation between movements therein, with lessons for transnational understandings of social movements, especially South-South movements.

Definite four-manifolds with exotic smooth structures

Abstract In this paper, we study smooth structures on closed, oriented four-manifolds with fundamental group Z / 2 ⁢ Z \mathbb{Z}/2\mathbb{Z} and definite intersection form. We construct infinitely many irreducible, oriented, closed, definite, smooth four-manifolds with π 1 = Z / 2 ⁢ Z \pi_{1}=\mathbb{Z}/2\mathbb{Z} and b 2 = 1 b_{2}=1 , and b 2 = 2 b_{2}=2 . As an application, we prove that, when the second Betti number b 2 b_{2} of a definite four-manifold with π 1 = Z / 2 ⁢ Z \pi_{1}=\mathbb{Z}/2\mathbb{Z} is positive and it admits a smooth structure, then it admits infinitely many smooth structures.

Circle-circle intersection. A universal method for solving typical surveying problems

AbstractThe research problem of the article is to devise a universal mathematical procedure for calculating point coordinates from typical planar surveying measurements. The proposed solution involves calculating the intersection points of two circles with radii equal to the measured distances (the distance-distance intersection problem). The author demonstrates a straightforward method for reducing every typical surveying problem to the distance-distance intersection form. The procedure also verifies the accuracy of the calculated coordinates. The derived equations were tested numerically using practical examples. The devised procedure will be integrated into an exhaustive numerical algorithm for diverse surveying problems regardless of the geometric approach during measurements.

Sexual Violence against Adults Aged 50 Years and Older and Implications for Prevention: A Thematic Analysis of Service Providers' Perceptions.

At-risk older adults and older survivors of sexual violence (SV) remain largely absent from SV prevention and intervention, owing to ageism and sexism, as well as other intersectional forms of prejudice, including among service providers (e.g., social workers, healthcare professionals, practitioners in SV organizations, and practitioners who serve older adults). This study explored perceptions, knowledge and experiences with SV against adults 50 years and older. Service providers who work with older adults and/or survivors were recruited, owing to where SV in later life is reported (e.g., healthcare, long-term care, and social service organizations, and to police in addition to SV service organizations), to contribute to the limited research in this area and to advance prevention and intervention. A survey was conducted on SV in later life, exploring knowledge, perceptions and experiences with SV in later life along with potential solutions for prevention and intervention among 126 service providers who worked with survivors and/or older adults. Their responses were thematically analyzed. Five themes were identified: (a) misconceptions of SV in later life and unique barriers to preventing it; (b) needs for knowledge, awareness, research and education; (c) policy and resource development; (d) victim blame and internalized stigma, and (e) ageism, intersectional prejudice and rape culture. The findings offer an in-depth understanding of barriers to prevention, and intervention, and multi-level recommendations for addressing them, which are provided by a diverse group of service providers who have worked with older adults and/or with survivors, reflecting multidisciplinary practice wisdom and experience.

On the intersection form of fillings

AbstractWe prove, by an ad hoc method, that exact fillings with vanishing rational first Chern class of flexibly fillable contact manifolds have unique integral intersection forms. We appeal to the special Reeb dynamics (stronger than ADC in [Lazarev, Geom. Funct. Anal. 30 (2020), no. 1, 188–254]) on the contact boundary, while a more systematic approach working for general ADC manifolds is developed independently by Eliashberg, Ganatra and Lazarev. We also discuss cases where the vanishing rational first Chern class assumption can be removed. We derive the uniqueness of diffeomorphism types of exact fillings of certain flexibly fillable contact manifolds and obstructions to contact embeddings, which are not necessarily exact.

Chow forms and complete intersections in the projective space

We prove that every Hodge cohomology class of bidegree (q,q) on a projective manifold X can be recovered from its image by the Chow transformation restricted to a suitable irreducible algebraic component of the space Cq−1(X) of effective algebraic cycles in X of dimension q−1. An application to the problem of the approximation by algebraic cycles is given. In the case of the cohomology class of an effective algebraic cycle, this injectivity at the cohomological level is a consequence of the inversion formula for the Chow transform of a conormal. When X=PN, the inversion formula for the conormal is extended to the case of the conormal of any closed positive (q,q)-current. An inversion formula for the Radon transform, defined on the Grassmannian, of smooth functions is involved and is also used to obtain a characterization of Chow forms of complete intersections in the projective space, expressed by means of the Capelli differential operators.

Those Lucky Enough to Transcend Gender: Travis Alabanza, Radical Transfeminism, and the Law

AbstractTravis Alabanza is a Black British transfeminine author and playwright, best known for their play Burgerz and their memoir None of the Above. This article places these works in conversation with the politics of radical transfeminism, a community-centred ethos which places above all the needs of marginalised transfeminine people, as they pertain to law and society. It engages themes of identity, violence, and legal regulation, and argues for a liberatory approach to trans life which does not depend on legal recognition for its legitimacy. It also discusses how radical transfeminism approaches intersectional forms of discrimination such as transmisogynoir by positing a different approach to legal and social structures.

Are Cities Doing the Same? Local Policies on Immigrant Integration in Catalonia Since the Great Recession

This article analyzes the extent to which the councils of five Catalan cities have modified their integration policies. The structural transformations of contemporary societies have had a great impact on city councils and local integration policies, especially from the point of view of planning and policy orientation. The article studies the policies developed in five Catalan cities in the last four mandates, specifically between 2007 and 2023, based on in-depth interviews and analysis of political and technical documentation. Although the strategies used in the five cities analyzed are not identical, the results show that during these years there has been a tendency to limit the approval of plans for the integration of immigrants, although this does not mean that the councils do not have explicit political priorities and objectives. The cities also tend to speak less specifically about integration and, on the contrary, resort to two different orientations: some councils design and implement policies related to security, mediation, and community work in neighborhoods, while others tend to broaden the focus of their policies, opting for more holistic approaches focused on multiple forms of diversity, intersectionality, and anti-racism.

Feminist Liberation Psychotherapy: Re-Politicizing Intersectionality Toward Socially Just Clinical Practice

Mainstream psychotherapy was not developed to address the harmful effects of systemic oppression. In addition to being largely rooted in Eurocentric values and knowledge systems, mainstream psychotherapy risks maintaining an unjust status quo rather than resisting and challenging sociopolitical oppression. Consequently, there is an urgent need for feminist intersectional models of healing that address sociopolitical power. We describe a liberation psychotherapy model that was developed to reconcile intersectional forms of power and foster conscientização, critical consciousness. This liberation psychotherapy model is theoretically grounded in liberation and critical-community psychologies and empirically derived out of qualitative data that explored expert therapists’ responsible navigation of intersectional power dynamics in feminist-multicultural and humanistic-existential psychotherapies. Liberation psychotherapists aim to empower clients’ exploration of their lived experiences through decolonial testimonio that supports liberatory transformation and social justice action. We illustrate examples of how a feminist liberation psychotherapy can be applied toward anti-racism and anti-oppression in clinical practice.

Applying an intersectional ecological framework to understand ableism and racism in employment among youth and young adults with disabilities

Purpose Youth with disabilities often face many barriers in finding employment. A knowledge gap exists surrounding the experiences of racially minoritized youth with disabilities who arguably encounter multiple and complex forms of discrimination. The purpose of this study was to understand the experiences of ableism and racism in employment among racially minoritized youth and young adults with non-apparent disabilities. Methods Individual semi-structured interviews were conducted with 19 racially minoritized participants aged 17—30 with non-apparent disabilities. Data were analyzed using a deductive thematic analysis approach informed by an intersectional ecological framework. Results Themes that affected racially minoritized youth’s employment included: (1) microsystems (i.e., individual barriers and facilitators to employment); (2) mesosystems (i.e., peers, family, disability, race/ethnicity, and work); (3) exosystems (i.e., workplace policies, healthcare system, educational institutions, community organizations); (4) macrosystems (i.e., ableism, racism, gendered discrimination and intersectional forms of discrimination); (5) the chronosystem (i.e., timing of obtaining employment, diagnosis and discrimination); and (6) ecological niche, which involved the extent to which work environments were safe and inclusive. Conclusion Applying an intersectional ecological framework facilitates our understanding of ableism and racism in employment among youth and young adults with disabilities. Further attention is urgently needed to minimize discrimination and enhance supportive, inclusive and psychologically safe, work environments for minoritized youth with disabilities.

Analysis on characteristics of ground vibration induced by underground high-speed trains based on in-situ test

With the increasingly emerging traffic intersection form of high-speed railways passing underneath integrated transport terminals, the ground vibration induced by trains running on underground high-speed railways has attracted extensive attention. In combination with the engineering example of a high-speed railway in construction passing underneath an airport, the wheel-drop impact test in the high-speed railway tunnel was designed to obtain the vibration characteristics of surrounding soil. The vehicle-track-tunnel-ground semi-analytical three-dimensional model was established to determine the initial dynamic load condition of the vehicle loads. The amplitude-frequency characteristic and transmission law of the ground vibration induced by trains running on underground high-speed railways were predicted and analyzed. The influences of different operation conditions, track parameters, and tunnel burial depths were compared. The research results show that the ground vibration obtained through the wheel-drop test is greatly attenuated within 10 m from the track centerline, with an attenuation rate up to 70%. The vertical vibration amplitude is obviously larger than that of the other two directions. The lateral ground vibration amplitude is the smallest with the slowest vibration attenuation speed. When the high-speed train passes through at the speed of 350 km/h, the vertical and lateral vibration levels of the ground surface within 80 m range are 20∼80 dB and 43∼72 dB, respectively. The maximum attenuation coefficient of Z-vibration level reaches 0.276 dB/m. For each increase of 50 km/h of the train speed, the Z-vibration level of the ground increases by about 2 dB. The smaller fastener stiffness leads to the greater ground vibration within 20∼50 Hz. The ground vibration level is positively correlated with the fastener stiffness above 79 Hz. When the burial depth of the tunnel is greater than 14 m, the burial depth of the tunnel has little effect on the change of the Z-vibration level of the ground.

Recentering and claiming joy and radical love in education

ABSTRACT Too often joy and radical love are brushed off to the side while addressing intersectional forms of supremacies within teacher education does not get addressed. While it is important to name systematic and intergenerational trauma and violence, building interdependence joy and radical love must be done alongside. We cannot dismantle and build if we do not know how to value ourselves. Using insights from auto-ethnographic approaches, we 1) define what a disability justice radical love approach, which centers joy, radical love, and the humanization of personal, professional, and programmatic identities, 2) illustrate how we started and continue to build such networks, and 3) offer strategic suggestions for centering joy and radical love within everyday educational practice — both on a micro and macro level — in building resistance, push back, and disruption of dehumanizing practices within teacher development and educational policy and practices.

Brieskorn spheres, cyclic group actions and the Milnor conjecture

AbstractIn this paper we further develop the theory of equivariant Seiberg–Witten–Floer cohomology of the two authors, with an emphasis on Brieskorn homology spheres. We obtain a number of applications. First, we show that the knot concordance invariants defined by the first author satisfy for torus knots, whenever is a prime not dividing . Since is a lower bound for the slice genus, this gives a new proof of the Milnor conjecture. Second, we prove that a free cyclic group action on a Brieskorn homology 3‐sphere does not extend smoothly to any homology 4‐ball bounding . In the case of a non‐free cyclic group action of prime order, we prove that if the rank of is greater than times the rank of , then the ‐action on does not extend smoothly to any homology 4‐ball bounding . Third, we prove that for all but finitely many primes a similar non‐extension result holds in the case that the bounding 4‐manifold has positive‐definite intersection form. Finally, we also prove non‐extension results for equivariant connected sums of Brieskorn homology spheres.

Rethinking peace and violence from the favelas

ABSTRACT This article reconsiders peace and security from the perspectives of community leaders, educators and activists in favelas in Rio de Janeiro, Brazil, in 2019–2020. Through a critical lens, it argues that the urban violence in Rio de Janeiro resembles a form of new wars where the state is a major producer of insecurity. It questions the meaning of peace and top-down pacification processes in a city where the favelas, since their origin, have been considered dangerous areas needing to be pacified and controlled. The article introduces favela peace formation as a concept to describe alternative processes working to reduce the intersectional forms of violence in these communities: non-violent, locally legitimate peace processes working to slowly construct a positive, sustainable peace. To conclude, it discusses how favela peace formation presents a way of imagining peace as ‘care’ instead of ‘order’ in response to the state’s violent peace as ‘control’.

Algebraic periods and minimal number of periodic points for smooth self-maps of 1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{1}$$\\end{document}-connected 4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{4}$$\\end{document}-manifolds with definite intersection forms

Let M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map f:M→M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f:M \\rightarrow M$$\\end{document}. This task is related to determining a topological invariant Dr4[f]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^4_r[f]$$\\end{document}, defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of iterations. Previously, the invariant was computed for self-maps of some 3-manifolds. In this paper, we compute the invariants Dr4[f]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^4_r[f]$$\\end{document} for the self-maps of closed 1-connected smooth 4-manifolds with definite intersection forms (i.e., connected sums of complex projective planes). We also present some efficient algorithmic approach to investigate that problem

A systematic literature review of intersectionality and disability in education

This systematic literature review synthesizes empirical analyses and applications of intersectionality in discussing disability in education. Even though intersectional methodologies have gained increased attention during the last decade, disability has rarely featured in these multi-axial analyses. The systematic review explores intersections of disability with other axes of identity and social disadvantage concerning perceptions and understandings of disability in education, experiences of ex/inclusion and educational dis/advantage. The review addresses the following questions: What intersectional dimensions of disability experience are explored? In what ways do students with disabilities experience intersectional forms of discrimination and oppression? What intersectionality-based education policy and practice implications are discussed in these articles? The review’s findings provide empirically tested insights into how the experience of disability is interwoven with and compounded by other markers of difference, while discussing implications for developing intersectionality-based policies and education research.

Contribution of the IATSS research projects to disseminating modern roundabouts in Japan

Until early 2000s, modern roundabouts (RABs) were poorly understood in Japan and were not fully recognized as a form of at-grade intersections. The RAB research projects of the International Association of Traffic and Safety Sciences (IATSS), which began in 2009, started with examining the applicability of RABs in Japan and have steadily progressed to various stages of field experiments, social implementation, and dissemination promotion activities. These RAB research projects, which lasted for approximately seven years, are considered to have played a significant role in the practical application of RAB in Japan. This paper provides a chronological overview of the history, content, and development status of these projects and records and discusses the role that IATSS research projects played in the early days of RABs in Japan.

Planning Application for Mobility Assessment of Intersection Forms in Intersection Control Evaluation

The use of alternative intersections and interchanges (AIIs) has proliferated significantly over the past two decades. Their introduction is motivated by the need to improve mobility and safety at conventional signalized and unsignalized intersections. This paper presents a mobility assessment component of the intersection control evaluation (ICE). The focus of this component was to develop a planning application and computational tools for the Stage II mobility analysis that can fill the current gap in coverage of the diverse (and expanding) suite of AIIs. The design of the tool prioritized the simultaneous analysis of multiple AIIs within the same platform using a common input dataset. This feature of the tool guarantees that alternative forms can be compared side-by-side under the same set of inputs and parameter assumptions using overall system delay as the key performance measure. In addition, the research developed a framework and movement definition scheme that enables the extension of the current platform to accommodate new and yet to be conceived innovative intersection forms. A comparison against two widely used commercial analytical platforms yielded virtually identical system delays and level of service ratings across 17 case studies covering eight different AII forms and under varying intersection congestion levels. The maximum system delay difference between the two methods was about 5 s, with an average absolute difference of less than 2.5 s. Future work will focus on expanding the tool to unsignalized versions of AIIs along with new and innovative forms that appear on the horizon.

Enumerating Calabi‐Yau Manifolds: Placing Bounds on the Number of Diffeomorphism Classes in the Kreuzer‐Skarke List

AbstractThe diffeomorphism class of simply connected smooth Calabi‐Yau threefolds with torsion‐free cohomology is determined via certain basic topological invariants: the Hodge numbers, the triple intersection form, and the second Chern class. In the present paper, we shed some light on this classification by placing bounds on the number of diffeomorphism classes present in the set of smooth Calabi‐Yau threefolds constructed from the Kreuzer‐Skarke (KS) list of reflexive polytopes up to Picard number six. The main difficulty arises from the comparison of triple intersection numbers and divisor integrals of the second Chern class up to basis transformations. By using certain basis‐independent invariants, some of which appear here for the first time, we are able to place lower bounds on the number of classes. Upper bounds are obtained by explicitly identifying basis transformations, using constraints related to the index of line bundles. Extrapolating our results, we conjecture that the favorable entries of the KS list of reflexive polytopes lead to some diffeomorphically distinct Calabi‐Yau threefolds.