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.
Electronic version of an article published as Journal of Knot Theory and Its Ramifications, 30(13), 2021, 2141008. https://doi.org/10.1142/S021821652141008X. © World Scientific Publishing Company. https://www.worldscientific.com/worldscinet/jktr
Kaiser, Uwe. (2021). "Homflypt Skein Theory, String Topology and 2-Categories". Journal of Knot Theory and Its Ramifications, 30(13), 2141008. https://doi.org/10.1142/S021821652141008X