HOMFLYPT Skein module of singular links
Luis Paris (IMB)
TL;DR
This paper computes the HOMFLYPT Skein module of singular links in the 3-sphere, utilizing Markov traces on singular Hecke algebras and classical skein techniques.
Contribution
It provides the first explicit calculation of the HOMFLYPT Skein module for singular links in the 3-sphere, connecting algebraic and topological methods.
Findings
Explicit computation of the skein module for singular links
Extension of Markov trace techniques to singular Hecke algebras
Discussion of open problems in singular Hecke algebra theory
Abstract
This paper is a presentation, where we compute the HOMFLYPT Skein module of singular links in the 3-sphere. This calculation is based on some results previously proved by Rabenda and the author on Markov traces on singular Hecke algebras, as well as on classical techniques that allow to pass from the framework of Markov traces on Hecke algebras to the framework of HOMFLYPT Skein modules. Some open problems on singular Hecke algebras are also presented.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Advanced Combinatorial Mathematics