Mapping Class Group Representations Derived from Stated Skein Algebras

TL;DR

This paper develops finite-dimensional projective representations of surface mapping class groups using stated skein algebras, advancing the understanding of algebraic structures associated with surface topology.

Contribution

It introduces a novel method to construct these representations from stated skein algebras, linking algebraic and topological properties.

Findings

Constructed finite-dimensional projective representations.

Established connections between skein algebras and mapping class groups.

Provided new tools for studying surface topology through algebra.

Abstract

We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algebras.