Homflypt skein theory, string topology and 2-categories

Abstract

We show that relations in Homflypt type skein theory of an oriented [Formula: see text]-manifold [Formula: see text] are induced from a [Formula: see text]-groupoid defined from the fundamental [Formula: see text]-groupoid of a space of singular links in [Formula: see text]. 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 [Formula: see text]-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.