HOMFLY-PT skein module of singular links in the three-sphere

Luis Paris (Institut de Mathematiques de Bourgogne)

Monday 12th May, 2014 16:00-17:00 Maths 204


HOMFLY-PT Skein modules are invariants which can be thought as a way to extend to three manifolds or to other knot-like objects (such as the singular links) classical knot invariants such as the HOMFLY-PT polynomial, the Jones polynomial or the Conway polynomial.
For a ring R, we denote by R[L] the free R-module spanned by the isotopy classes of singular links in S^3.
Given two invertible elements x,t in R, the HOMFLY-PT skein module of singular links in S^3 (relative to the triple (R,t,x)) is the quotient of R[L] by local relations, called skein relations, that involve t and x.
The aim of this lecture is to show how to compute this module by means of very simple techniques.

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