Classical shadows of stated skein representations at roots of unity
Geometric Topology
2024-07-24 v3 Algebraic Topology
Abstract
We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1 embeds canonically into the centers of the stated skein algebras whose deforming parameter is an odd root unity. We also construct an isomorphism between the stated skein algebra at +1 and the algebra of regular function of a generalization of the SL2-character variety of the surface. As a result, we associate to each isomorphism class of irreducible or local representations of the stated skein algebra, an invariant which is a point in the character variety.
Cite
@article{arxiv.1905.03441,
title = {Classical shadows of stated skein representations at roots of unity},
author = {Julien Korinman and Alexandre Quesney},
journal= {arXiv preprint arXiv:1905.03441},
year = {2024}
}