Twist Knots Research Articles

The Asymptotics of the Higher Dimensional Reidemeister Torsion for Exceptional Surgeries Along Twist Knots

AbstractWe determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL2()-representations of the graph manifold are induced by irreducible metabelian representations of the twist knot group. We also give the set of the limits of the leading coeõcients in the higher dimensional Reidemeister torsion explicitly.

Journal positioning meta-issues as evolving contexts: Organizational marketing at the crossroads

As Industrial Marketing Management (IMM) has completed 45 years of publication, Industrial Marketing Management: An Interorganizational Interdisciplinary Journal comes of age yet again. A description of the proliferation of journals and associated titles within cognate subfields is provided noting the societal forces creating this necessity. Relief is brought to the complexity and diversity of journals therein. The unit of analysis is that of an individual circumspect scholar viewing the journal mix landscape and its associated impact on their scholarship and career. Contexts and criteria are offered for sorting out this meta-dilemma that has been evolving since time immemorial. Peter J. LaPlaca's (PJL's) presence in our field and IMM is explicated with awe and appreciation. Closing thoughts are offered regarding our collective future and some criteria for getting there – the next interlude. The reader is invited to ascertain their unique scholarly path.Both quantitative and qualitative analyses are used in the evaluation of the mere incidence of article outlets and the moderating effect on institutional and industry constraints as accelerated over the past 45 years. Industry sources that measure and monitor journal use and their activity are broadly and succinctly portrayed.Historical analyses of college business school education's evolution with the associated impact of these industrial forces for journal publishing are derived. A narrative describing the evolution in the quantity of journals and their proliferation is provided. The analysis is by definition contemporary yet retrospective, qualitative yet adductive. PJL's long-term contribution to the field is documented with awe and appreciation.Individual scholars are to know that their own acumen and that of those whom they may come to supervise are constrained yet enabled by the mere quantity of journal options and their inevitable domain enmeshment. The impact on education and the management thereof are noted in detail and associated sense making in the performance of our job.The analyses of the journals publishing provides a paradox of opportunity yet a twisted knot of options for any scholar requiring yet further criteria to untie. Over most of our career lifespans the data and analysis provided help contextualize the character of your scholarly journey. A glimpse into the evolution of research in the area of business-to-business marketing and its components over the last few decades helps magnify the positioning of the journals for prospective authors and would-be readers.

HOMFLY for twist knots and exclusive Racah matrices in representation [333

Next step is reported in the program of Racah matrices extraction from the differential expansion of HOMFLY polynomials for twist knots: from the double-column rectangular representations R=[rr] to a triple-column and triple-hook R=[333]. The main new phenomenon is the deviation of the particular coefficient f[332][21] from the corresponding skew dimension, what opens a way to further generalizations.

Composite Knots Obtained by Twisting Torus Knots

Abstract A twisted torus knot is obtained from a torus knot by performing full twists on some adjacent strands of the torus knot. Morimoto constructed infinitely many twisted torus knots which are composite knots and he conjectured that his knots are all of composite twisted torus knots. We show that his conjecture is almost true by giving a complete list of such twisted torus knots.

The use of orthopaedic wire for fracture fixation in companion animals

Orthopaedic wire is widely used in companion animal fracture repair. It is mainly applied as an auxiliary fixation method, in combination with other orthopaedic implants, and rarely as the sole method of fixation. The most frequently used types of orthopaedic wire are those with both ends straight, and the AO/ASIF wire, which has an "eye" twisted into one end of it, whereas the other end is straight. The wire should be applied tighdy and secured into place, either by a twist knot or by the use of a locking loop, respectively. Three types of wiring can be seen: fullcerclage wire, tension band wire and interfragmentary wires (cruciate or hemi-cerclage). The understanding of the proper principles of orthopaedic wire application and of the limitations of its use with fracture management is crucial. When applied properly and in the correct circumstances, orthopaedic wire is an effective mean of fracture fixation.

On certain 𝐿-functions for deformations of knot group representations

We study the twisted knot module for the universal deformation of an SL 2 \textrm {SL}_2 -representation of a knot group and introduce an associated L L -function, which may be seen as an analogue of the algebraic p p -adic L L -function associated to the Selmer module for the universal deformation of a Galois representation. We then investigate two problems proposed by Mazur: Firstly we show the torsion property of the twisted knot module over the universal deformation ring under certain conditions. Secondly we compute the L L -function by some concrete examples for 2 2 -bridge knots.

Volumes of hyperbolic double twist knot cone-manifolds

We give explicit formulas for the volumes of hyperbolic cone-manifolds of double twist knots, a class of two-bridge knots which includes twist knots and two-bridge knots with Conway notation [Formula: see text]. We also study the Riley polynomial of a class of one-relator groups which includes two-bridge knot groups.

Additional cases of positive twisted torus knots

A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in [Formula: see text], the genus 2 Heegaard surface for [Formula: see text]. Primitive/primitive and primitive/Seifert knots lie in [Formula: see text] in a particular way. Dean gives sufficient conditions for the parameters of the twisted torus knots to ensure they are primitive/primitive or primitive/Seifert. Using Dean’s conditions, Doleshal shows that there are infinitely many twisted torus knots that are fibered and that there are twisted torus knots with distinct primitive/Seifert representatives with the same slope in [Formula: see text]. In this paper, we extend Doleshal’s results to show there is a four parameter family of positive twisted torus knots. Additionally, we provide new examples of twisted torus knots with distinct representatives with the same surface slope in [Formula: see text].

Branched twist spins and knot determinants

A branched twist spin is a generalization of twist spun knots, which appeared in the study of locally smooth circle actions on the $4$-sphere due to Montgomery, Yang, Fintushel and Pao. In this paper, we give a sufficient condition to distinguish non-equivalent, non-trivial branched twist spins by using knot determinants. To prove the assertion, we give a presentation of the fundamental group of the complement of a branched twist spin, which generalizes a presentation of Plotnick, calculate the first elementary ideals and obtain the condition of the knot determinants by substituting $-1$ for the indeterminate.

A twisted link invariant derived from a virtual link invariant

Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a possibly non-orientable surface. In this paper, we discuss an invariant of twisted links which is obtained from the JKSS invariant of virtual links by use of double coverings. We also discuss some properties of double covering diagrams.

Axis systems of link projections

An axis of a link projection is a closed curve which lies symmetrically on each region of the link projection. In this paper we define axis systems of link projections and characterize axis systems of the standard projections of twist knots.

The shrinkage type of knots

We study spectral gaps of cellular differentials for finite cyclic coverings of knot complements. Their asymptotics can be expressed in terms of irrationality exponents associated with ratios of logarithms of algebraic numbers determined by the first two Alexander polynomials. From this point of view, it is natural to subdivide all knots into three different types. We show that examples of all types abound and discuss what happens for twist and torus knots as well as knots with few crossings.

The Alexander polynomial for virtual twist knots

We define a family of virtual knots generalizing the classical twist knots. We develop a recursive formula for the Alexander polynomial [Formula: see text] (as defined by Silver and Williams [Polynomial invariants of virtual links, J. Knot Theory Ramifications 12 (2003) 987–1000]) of these virtual twist knots. These results are applied to provide evidence for a conjecture that the odd writhe of a virtual knot can be obtained from [Formula: see text].

Satellite Knots Obtained by Twisting Torus Knots: Hyperbolicity of Twisted Torus Knots

Satellite Knots Obtained by Twisting Torus Knots: Hyperbolicity of Twisted Torus Knots

Reidemeister Torsion and Dehn Surgery on Twist Knots

We compute the Reidemeister torsion of the complement of a twist knot in $S^3$ and that of the 3-manifold obtained by a $\frac{1}{q}$-Dehn surgery on a twist knot.

On rectangular HOMFLY for twist knots

As a new step in the study of rectangularly-colored knot polynomials, we reformulate the prescription [A. Morozov, arXiv:1606.06015v8 ] for twist knots in the double-column representations [Formula: see text] in terms of skew Schur polynomials. These, however, are mysteriously shifted from the standard topological locus, which makes further generalization to arbitrary [Formula: see text] not quite straightforward.

Some families of minimal elements for a partial ordering on prime knots

We show that all twist knots and certain double twist knots are minimal elements for a partial ordering on the set of prime knots. The keys to these results are presentations of their character varieties using Chebyshev polynomials and a criterion for irreducibility of a polynomial of two variables. These give us an elementary method to discuss the number of irreducible components of the character varieties, which concludes the result essentially.

Factorization of differential expansion for antiparallel double-braid knots

Continuing the quest for exclusive Racah matrices, which are needed for evaluation of colored arborescent-knot polynomials in Chern-Simons theory, we suggest to extract them from a new kind of a double-evolution -- that of the antiparallel double-braids, which is a simple two-parametric family of two-bridge knots, generalizing the one-parametric family of twist knots. In the case of rectangular representations $R=[r^s]$ we found an evidence that the corresponding differential expansion miraculously factorizes and can be obtained from that for the twist knots. This reduces the problem of rectangular exclusive Racah to constructing the answers for just a few twist knots. We develop a recent conjecture on the structure of differential expansion for the simplest members of this family (the trefoil and the figure-eight knot) and provide the exhaustive answer for the first unknown case of $R=[33]$. The answer includes HOMFLY of arbitrary twist and double-braid knots and Racah matrices $\bar S$ and $S$ -- what allows to calculate $[33]$-colored polynomials for arbitrary arborescent (double-fat) knots. For generic rectangular representations described in detail are only the contributions of the single- and two-floor pyramids, the way to proceed is explicitly illustrated by the examples of $R=[44]$ and $R=[55]$. This solves the difficult part of the problem, but the last tedious step towards explicit formulas for generic exclusive rectangular Racah matrices still remains to be made.

Explicit formulae for Chern-Simons invariants of the twist-knot orbifolds and edge polynomials of twist knots

We calculate the Chern-Simons invariants of twist-knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of twist knot cone-manifold structures. Following the general instruction of Hilden, Lozano, and Montesinos-Amilibia, we here present concrete formulae and calculations. We use the Pythagorean Theorem, which was used by Ham, Mednykh and Petrov, to relate the complex length of the longitude and the complex distance between the two axes fixed by two generators. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic twist-knot orbifolds. We also derive some interesting results. The explicit formulae of the -polynomials of twist knots are obtained from the complex distance polynomials. Hence the edge polynomials corresponding to the edges of the Newton polygons of the -polynomials of twist knots can be obtained. In particular, the number of boundary components of every incompressible surface corresponding to slope turns out to be . Bibliography: 39 titles.

On nonabelian representations of twist knots

On nonabelian representations of twist knots