Relating quantum character varieties and skein modules
Julien Korinman, Jun Murakami
TL;DR
This paper establishes connections between skein modules and quantum representation spaces, providing new descriptions of their classical limits and topological properties of 3-manifolds.
Contribution
It introduces a novel relation between skein modules and quantum representations, leading to new theorems and descriptions of skein modules of mapping tori and link exteriors.
Findings
Relation between skein modules and quantum representation spaces
Quantum Van Kampen and HNN extension theorems for skein modules
New descriptions of skein modules of mapping tori and links
Abstract
We relate the Kauffman bracket stated skein modules to two independent constructions of quantum representation spaces of Habiro and Van der Veen with the second author. We deduce from this relation a description of the classical limit of stated skein modules, a quantum Van Kampen theorem and a quantum HNN extension theorem for stated skein modules and obtain a new description of the skein modules of mapping tori and links exteriors.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Operator Algebra Research · Geometric and Algebraic Topology