Algebraic generators of the skein algebra of a surface

Santharoubane, Ramanujan

doi:10.2140/agt.2024.24.2571

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Algebraic generators of the skein algebra of a surface

Ramanujan Santharoubane

Algebraic & Geometric Topology 24 (2024) 2571–2578

DOI: 10.2140/agt.2024.24.2571

Abstract

Let $Σ$ be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the Kauffman bracket 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 $Σ$ .

Keywords

skein algebra, 3–manifold

Mathematical Subject Classification

Primary: 57K31

References

Publication

Received: 4 March 2022

Revised: 21 November 2022

Accepted: 13 December 2022

Published: 19 August 2024

Authors

Ramanujan Santharoubane
Laboratoire Mathématiques d’Orsay, CNRS Université Paris-Saclay Orsay France	Department of Mathematics University of Virginia Charlottesville, VA United States

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Volume 24, issue 5 (2024)