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Homflypt skein theory, string topology and $2$ $2$ -categories

Uwe Kaiser

Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725-1555, USA

https://doi.org/10.1142/S021821652141008XCited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue — Dedicated to the 60th Birthday of J. H. Przvtycki
Guest Editors: M. K. Dabkowski, V. Harizanov, L. H. Kauffman, J. H. Przytycki, R. Sazdanovic and A. Sikora

Abstract

We show that relations in Homflypt type skein theory of an oriented $3$ $3$ -manifold $M$ $M$ are induced from a $2$ $2$ -groupoid defined from the fundamental $2$ $2$ -groupoid of a space of singular links in $M$ $M$ . 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 $2$ $2$ -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.

Keywords:

AMSC: 57M25, 57M27

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Vol. 30, No. 13

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History

Received 3 September 2019

Revised 2 October 2019

Accepted 5 March 2021

Published: 26 February 2022

Keywords

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Homflypt skein theory, string topology and $2$ $2$ -categories

Abstract

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System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Homflypt skein theory, string topology and 22<math altimg="eq-00001.gif" display="inline"><mn>2</mn></math>-categories

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