Homflypt Skein Theory, String Topology and 2-Categories

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Abstract

We show that relations in Homflypt type skein theory of an oriented 3-manifold M are induced from a 2-groupoid defined from the fundamental 2-groupoid of a space of singular links M . The module relations are defined by homomorphisms related to string topology. They appear from a representation of the groupoid into free modules on a set of model objects. The construction on the fundamental 2-groupoid is defined by the singularity stratification and relates Vassiliev and skein theory. Several explicit properties are discussed, and some implications for skein modules are derived.

Original languageAmerican English
JournalMathematics Faculty Publications and Presentations
StatePublished - 1 Nov 2021

Keywords

  • 2-category
  • 3-manifold
  • Vassiliev invariants
  • skein modules

EGS Disciplines

  • Mathematics

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