Loop Space Research Articles

Clinical assessment of the abutment teeth of children undergoing space maintainer therapy: A randomised controlled trial

Introduction: The band and loop space maintainer are one of the most commonly used fixed space maintainers in children. However, prolonged use of appliances in the oral cavity may lead to changes in gingival health and an increased risk of caries. Objectives: This study aims to evaluate the clinical parameters of the abutment teeth, specifically the banded teeth and the tooth to which the loop is extended. Methods: This prospective clinical study included 35 children between the age group of 5 to 9 years. The children were examined at baseline and 6-month follow-up. The abutment teeth were evaluated on bleeding on probing, pocket depth, gingival index, and occurrence of primary/ secondary caries. Results: There was a significant difference in the bleeding on probing, pocket depth, gingival index, and occurrence of primary/ secondary caries (p<0.05). Conclusion: Precautions and thorough knowledge about the consequences of the delivery of appliances can prevent and overcome the causes. Oral health education and constant motivation should be provided to the children on dental hygiene and regular follow-ups to avoid any extensive invasive management.

The Lubin–Tate theory of configuration spaces: I

AbstractWe construct a spectral sequence converging to the Lubin–Tate theory, that is, Morava ‐theory, of unordered configuration spaces and identify its ‐page as the homology of a Chevalley–Eilenberg‐like complex for Hecke Lie algebras. Based on this, we compute the ‐theory of the weight summands of iterated loop spaces of spheres (parameterizing the weight operations on ‐algebras), as well as the ‐theory of the configuration spaces of points on a punctured surface. We read off the corresponding Morava ‐theory groups, which appear in a conjecture by Ravenel. Finally, we compute the ‐homology of the space of unordered configurations of particles on a punctured surface.

On the topology of loops of contactomorphisms and Legendrians in non-orderable manifolds

We study the global topology of the space L of loops of contactomorphisms of a non-orderable closed contact manifold (M2n+1,ξ). We filter L by a quantitative measure of the “positivity” of the loops and describe the topology of L in terms of the subspaces of the filtration. In particular, we show that the homotopy groups of L are subgroups of the homotopy groups of the subspace of positive loops L+. We obtain analogous results for the space of loops of Legendrian submanifolds in (M2n+1,ξ).

Fracture Resistance of Space Maintainers Produced Using 3D Printable Materials.

This study aimed to evaluate the fracture resistance of space maintainers (SMs) produced using 3D-printable materials (metal, resin and polyetheretherketone [PEEK]) after thermal aging and compare them with conventional space maintainers. A standardised typodont model for paediatric dentistry was utilised, and band and loop space maintainers were designed digitally using computer-aided design (CAD) technology. Four groups were established: Conventional, 3D printed metal, 3D printed resin, and 3D printed PEEK. Fracture resistance was assessed after 10,000 thermal cycles, simulating oral conditions. Fracture tests were conducted using a universal testing machine, applying vertical force to the band and loop junction until fracture. Statistical analyses were performed using one-way ANOVA and the Tukey HSD test (P<0.05). Although the fracture resistance values showed that metal, resin, and PEEK 3D printed band and loop space maintainers can be acceptable clinically, the permanent resin may be preferable to printable material because of their aesthetic properties.

The (1,0) tensor and hypermultiplets in loop space

We show that the (1,0) tensor and hypermultiplet supersymmetry variations can be uplifted to loop space. Upon dimensional reduction we make contact with abelian five-dimensional super Yang-Mills, which has a nonabelian generalization that we subsequently uplift back to loop space where we conjecture a nonabelian generalization of the (1,0) supersymmetry variations and demonstrate their on-shell closure.

Clinical Effectiveness of Various Unilateral Fixed Space Maintainers vs Band and Loop Space Maintainers in Mixed Dentition: A Systematic Review

Clinical Effectiveness of Various Unilateral Fixed Space Maintainers vs Band and Loop Space Maintainers in Mixed Dentition: A Systematic Review

An index theorem for loop spaces

We formulate and prove an index theorem for loop spaces of compact manifolds in the framework of KK-theory. It is a strong candidate for the noncommutative geometrical definition (or the analytic counterpart) of the Witten genus. In order to specify an “appropriate form” of the index theorem to formulate a loop space version, we formulate and prove an equivariant index theorem for non-compact S1-manifolds with a compact fixed-point set. In order to formulate it, we use a ring of formal power series.

Assessment of Knowledge and Utilization of Prefabricated Band and Loop Space Maintainers in Primary Dentition Among Dentists: A Cross-Sectional Questionnaire Study.

Preserving primary dentition is essential for maintaining optimal oral health and development in children. Premature loss of primary teeth due to caries, infection, crowding, or trauma can necessitate orthodontic intervention and lead to various complications. Space maintainers are critical for preserving arch space until the eruption of permanent teeth, thereby preventing issues such as ectopic eruption, crowding, and malocclusion. Despite their advantages, prefabricated space maintainers (PSMs) are underutilized. This study aims to evaluate the knowledge, attitudes, and practices of Indian dentists regarding PSMs in primary teeth. A cross-sectional questionnaire survey was conducted among 100 dental practitioners in Chennai. A 10-item self-administered questionnaire, developed based on a comprehensive literature review and expert consultations, assessed demographics, knowledge of PSM indications and techniques, current practices, perceived barriers, and preferences for continuing education. The questionnaire's reliability was confirmed with a Cronbach's alpha value of 0.85. Descriptive statistics, including frequencies andpercentages, were used to summarize the participants' demographic characteristics, knowledge levels, and current practices related to PSMs. Of the 100 respondents, 86 (86%) were males and 14 (14%) were females. Only 19 (19%) reported using PSMs, while 36 (36%) used conventional space maintainers. A significant proportion (42 (42%)) of the respondents held a master's degree in dental surgery, yet only 11 (11%) had participated in Continuing Dental Education (CDE) programs on space maintainers. The perceived benefit of PSMs being a single appointment procedure was acknowledged by 82 (82%) of the respondents, whereas 76 (76%) participants identified cost as a major drawback. Notably, 45 (45%) practitioners did not consider PSMs necessary. This survey highlights notable obstacles in the adoption of PSMs among Indian dentists, emphasizing the need for focused educational initiatives. Improving knowledge and practices related to PSMs can enhance pediatric dental care and oral health outcomes in India.

Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups

Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups

Homotopy Theoretic Properties Of Open Books

ABSTRACT We study the homotopy groups of open books in terms of those of their pages and bindings. Under homotopy theoretic conditions on the monodromy we prove an integral decomposition result for the based loop space on an open book, and under more relaxed conditions we prove a rational loop space decomposition. The latter case allows for a rational dichotomy theorem for open books, as an extension of the classical dichotomy in rational homotopy theory. As a direct application, we show that for Milnor’s open book decomposition of an odd sphere with monodromy of finite order the induced action of the monodromy on the homology groups of its page cannot be nilpotent.

Connes fusion of spinors on loop space

The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the description of two-dimensional sigma models as the bundle of states over the configuration space of the superstring. We construct a product on this bundle that covers the fusion of loops, i.e. the merging of two loops along a common segment. For this purpose, we exhibit it as a bundle of bimodules over a certain von Neumann algebra bundle, and realize our product fibrewise using the Connes fusion of von Neumann bimodules. Our main technique is to establish novel relations between string structures, loop fusion, and the Connes fusion of Fock spaces. The fusion product on the spinor bundle on loop space was proposed by Stolz and Teichner as part of a programme to explore the relation between generalized cohomology theories, functorial field theories, and index theory. It is related to the pair of pants worldsheet of the superstring, to the extension of the corresponding smooth functorial field theory down to the point, and to a higher-categorical bundle on the underlying string manifold, the stringor bundle.

Effectiveness of traditional band and loop space maintainer vs 3D-printed space maintainer following the loss of primary teeth: a randomized clinical trial

This study evaluates the efficacy of 3D-printed band and loop space maintainers (3D-BLSMs) to mitigate concerns caused by early primary tooth loss in children when compared to their conventional equivalents. Over 9 months, 62 participants aged 6 to 12 years participated in a randomized clinical study. This study evaluated their failure rates (de-cementation, debonding, solder breakage, loop breakage, band breakage, and abutment tooth fracture), gingival health, and patient overall satisfaction. Random assignments were made to place the participants in two groups: traditional band and loop space maintainers or the 3D-BLSMs. The findings show that at 9 months, 3D-BLSMs provided significantly higher survival rates (77.4%) than conventional maintainers (51.6%, p < 0.01). Gum inflammation was mild in both groups, highlighting the need for good oral hygiene. In both groups, patient satisfaction exceeded 90%. Although there was some pain at first with 3D-BLSMs, this eventually subsided and aesthetic preferences disappeared. There were no negative consequences noted, and both groups needed ongoing dental treatment. In conclusion, with excellent patient satisfaction in both groups, 3D-printed space maintainers offer greater long-term durability in reducing dental concerns following early primary tooth loss.

The Morse Index for Manifolds with Constant Sectional Curvature

We compute the Morse index of a critical submanifold of the energy functional on the loop space of a manifold with constant sectional curvature. The case of constant non-positive sectional curvature is a known result and the case of a sphere has been proved by Klingenberg. We adapt Klingenberg’s proof of the case of a sphere to the case of constant sectional curvature, to obtain the possible Morse indices of critical submanifolds of the energy functional.

Factors Influencing the Fit and Retention of Computer-aided Design/Computer-aided Manufacturing-based Three-dimensional Printed Band and Loop Space Maintainers.

Tirupathi S, Rathi N. Factors Influencing the Fit and Retention of Computer-aided Design/Computer-aided Manufacturing-based Three-dimensional Printed Band and Loop Space Maintainers. Int J Clin Pediatr Dent 2024;17(6):734-735.

Chromatic Cardinalities via Redshift

Abstract Using higher descent for chromatically localized algebraic $K$-theory, we show that the higher semiadditive cardinality of a $\pi $-finite $p$-space $A$ at the Lubin–Tate spectrum $E_{n}$ is equal to the higher semiadditive cardinality of the free loop space $LA$ at $E_{n-1}$. By induction, it is thus equal to the homotopy cardinality of the $n$-fold free loop space $L^{n} A$. We explain how this allows one to bypass the Ravenel–Wilson computation in the proof of the $\infty $-semi-additivity of the ${T(n)} $-local categories. “Cardinalis sinuatus – the Pyrrhuloxia” by Dick Culbert licensed under CC BY 2.0.

The stable Picard group of finite Adams Hopf algebroids with an application to the [formula omitted]-motivic Steenrod subalgebra [formula omitted]

In this paper, we investigate the rigidity of the stable comodule category of a specific class of Hopf algebroids known as finite Adams, shedding light on its Picard group. Then, we establish a reduction process through base changes, enabling us to effectively compute the Picard group of the ▪-motivic mod 2 Steenrod subalgebra▪. Our computation shows that ▪ is isomorphic to ▪, where two ranks come from the motivic grading, one from the algebraic loop functor, and the last is generated by the ▪-motivic joker J.

Topological aspects of brane fields: Solitons and higher-form symmetries

In this note, we classify topological solitons of n-brane fields, which are nonlocal fields that describe n-dimensional extended objects. We consider a class of n-brane fields that formally define a homomorphism from the n-fold loop space \Omega^n X_DΩnXD of spacetime X_DXD to a space Ε_nΕn. Examples of such n-brane fields are Wilson operators in n-form gauge theories. The solitons are singularities of the n-brane field, and we classify them using the homotopy theory of E_nEn-algebras. We find that the classification of codimension {k+1}k+1 topological solitons with {k≥ n}k≥n can be understood using homotopy groups of \mathcal{E}_nℰn. In particular, they are classified by {\pi_{k-n}(\mathcal{E}_n)}πk−n(ℰn) when {n&gt;1}n&gt;1 and by {\pi_{k-n}(\mathcal{E}_n)}πk−n(ℰn) modulo a {\pi_{1-n}(\mathcal{E}_n)}π1−n(ℰn) action when {n=0}n=0 or {1}1. However, for {n&gt;2}n&gt;2, their classification goes beyond the homotopy groups of \mathcal{E}_nℰn when k &lt; n, which we explore through examples. We compare this classification to n-form \mathcal{E}_nℰn gauge theory. We then apply this classification and consider an {n}n-form symmetry described by the abelian group {G^{(n)}}G(n) that is spontaneously broken to {H^{(n)}\subset G^{(n)}}H(n)⊂G(n), for which the order parameter characterizing this symmetry breaking pattern is an {n}n-brane field with target space {\mathcal{E}_n = G^{(n)}/H^{(n)}}ℰn=G(n)/H(n). We discuss this classification in the context of many examples, both with and without ’t Hooft anomalies.

On multiplicative spectral sequences for nerves and the free loop spaces

We construct a multiplicative spectral sequence converging to the cohomology algebra of the diagonal complex of a bisimplicial set with coefficients in a field. The construction provides a spectral sequence converging to the cohomology algebra of the classifying space of a category internal to the category of topological spaces. By applying the machinery to a Borel construction, we explicitly determine the mod p cohomology algebra of the free loop space of the real projective space for each odd prime p. This example is emphasized as an important computational case. Moreover, we represent generators in the singular de Rham cohomology algebra of the diffeological free loop space of a non-simply connected manifold M with differential forms on the universal cover of M via Chen's iterated integral map.

Comparative Evaluation of Gingival Health Among Children With Stainless Steel Crowns and Stainless Steel Bands: A Split-Mouth Randomized Controlled Trial.

Introduction Putting in stainless steel crowns as a post-endodontic restoration and space maintainers as a post-extraction applianceto maintain the space for the eruption of underlying teeth in case of early loss in children are some of the most commonly practised proceduresthat pediatric dentists undertake in their day-to-day lives. Maintaining good oral hygiene for better gingival health is important. If it is not taken care of,gradual destruction of supporting soft and hard tissues of the teeth occurs. There were numerous studies conducted over the past few years,but no split-mouth study compares the crowns and bands. Hence, this study compares the gingival health between stainless steel crowns and band and loop space maintainers. Materials and methods This split-mouth randomised controlled trial included 31 children aged between four and nine years who had stainless steel crowns on one side and a band and loop space maintainer on the other side of the mandibular arch. The split-mouth study was carried out to minimise the outcome bias as oral hygiene practices differ from one individual to another. Presence/absence of bleeding on probing (BOP)and the Gingival Index (GI) using theLoeandSilness GI were assessed at baseline and at six months. Data was entered in an Excel sheet (Microsoft Corporation,Redmond, Washington, United States) and analysed in IBMSPSSStatistics for Windows, Version 23, (Released 2015; IBM Corp., Armonk, New York, United States). The significance level was fixed as 5% (α = 0.05). The Shapiro-Wilktest was used to assess the normality of parameters of gingival health. The parameters are described in terms of mean, standard deviation, frequency and percentages. Intragroup analysis was done using Friedman tests across the timelines. Intergroup analysis using Mann-Whitney U tests was done between the groups at different timelines. Results At the beginning of the study, 46 children (22 girlsand 24 boys) were enrolled considering the dropout. However, 15 children did not attend the follow-up review, resulting in a loss to follow-up. Consequently, only 31 children, each with a band and loop space maintainer and a stainless steel crown, were included for the final interpretation of the results in this study. At one month, both BOP and GI were significantly different (p<0.05) between the stainless steelcrown and stainless steel band where the crown showed better gingival health and absence of bleeding than the band and loop. At three months and six months, gingival health improved in both groups, but there was no significant difference between the groups. The Friedman test revealed that both the stainless steel crown and stainless steel band groups had a significant difference at six months from baseline. Mann-Whitney tests were done to analyse the difference in parameters at baseline and at six months between both groups. There was no significant difference in the baseline in the parameters between the groups. Conclusion Within the limitations of the study, this study concludes that the gingival health based on BOP and GI shows a significant difference across the timeline within the groups, namely, stainless steel crown and stainless steel band, but no significant difference between the groups at various timelines.

Loop Space Decompositions of Moment-Angle Complexes Associated to Flag Complexes

Abstract We prove that the loop space of the moment-angle complex associated with the k-skeleton of a flag complex belongs to the class $\mathcal{P}$ of spaces homotopy equivalent to a finite-type product of spheres and loops on simply connected spheres. To do this, a general result showing $\mathcal{P}$ is closed under retracts is proved.