Results 1 to 10 of about 253 (87)
Quandle and Biquandle Homology Calculation in R
Journal of Open Research Software, 2018 In knot theory several knot invariants have been found over the last decades. This paper concerns itself with invariants of several of those invariants, namely the Homology of racks, quandles, biracks and biquandles.
Roger Fenn, Ansgar Wenzel
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Primary decomposition in the smooth concordance group of topologically slice knots
Forum of Mathematics, Sigma, 2021 We address primary decomposition conjectures for knot concordance groups, which predict direct sum decompositions into primary parts. We show that the smooth concordance group of topologically slice knots has a large subgroup for which the conjectures ...
Jae Choon Cha
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, 2002 Several authors have recently studied virtual knots and links because they admit invariants arising from R-matrices. We prove that every virtual link is uniquely represented by a link L SI in a thickened, compact, oriented surface S such that the link ...
G. Kuperberg
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Knot Floer homology and integer surgeries [PDF]
, 2004 Let Y be a closed three-manifold with trivial first homology, and let K Y be a knot. We give a description of the Heegaard Floer homology of integer surgeries on Y along K in terms of the filtered homotopy type of the knot invariant for K .
P. Ozsváth, Z. Szabó
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Torus knots and quantum modular forms [PDF]
, 2014 In this paper we compute a q-hypergeometric expression for the cyclotomic expansion of the colored Jones polynomial for the left-handed torus knot (2,2t+1). We use this to define a family of q-series, the simplest case of which is the generating function
K. Hikami, Jeremy Lovejoy
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Extended Bloch group and the Cheeger-Chern-Simons class [PDF]
, 2003 We dene an extended Bloch group and show it is naturally isomorphic to H3(PSL(2;C);Z). Using the Rogers dilogarithm function this leads to an exact simplicial formula for the universal Cheeger{Chern{Simons class on this homology group.
W. Neumann
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On the torsional energy of torus knots under infinitesimal bending
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 The article deals with the infinitesimal bending theory application to the knots theory. The impact of infinitesimal bending on the torsional energy at torus knots is considered, and the results show that it is not stationary under infinitesimal bending.
Maksimović Miroslav D. +4 more
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A categorification for the chromatic polynomial [PDF]
, 2004 For each graph we construct graded cohomology groups whose graded Euler characteristic is the chromatic polynomial of the graph. We show the cohomology groups satisfy a long exact sequence which corre- sponds to the well-known deletion-contraction rule ...
Laure Helme-Guizon, Yongwu Rong
semanticscholar +1 more source
Minimal surface representations of virtual knots and links [PDF]
, 2004 Kuperberg (15) has shown that a virtual knot diagram corre- sponds (up to generalized Reidemeister moves) to a unique embedding in a thickened surface of minimal genus. If a virtual knot diagram is equivalent to a classical knot diagram then this minimal
H. A. Dye, L. Kauffman
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Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 954-1032, October 2020., 2020 Abstract I provide an explicit construction of spectral curves for the affine E8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the representation ring of E8 for the exterior algebra of the adjoint representation; this is in turn employed to provide an explicit construction of ...
Andrea Brini
wiley +1 more source