Work

Algebraic generators of the skein algebra of a surface

Year: 2024

Type: article

Abstract: Let $Σ$ be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the skein algebra of $Σ$ over the field of rational functions can be algebraically generated by a finite number of simple closed curves that are naturally associated to certain generators of the mapping class group of $Σ$. The action of the mapping class group on the skein algebra gives canonical relations between these generators. From this, we conjecture a presentation for a skein algebra of $Σ$.

Source: Algebraic & Geometric Topology

Author: Ramanujan Santharoubane

Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay, University of Virginia

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W2794865611

FWCI: 2.028

Cites: 11

Cited by: 6

Related to: 10