Representations of the Kauffman bracket skein algebra, II: Punctured surfaces

Bonahon, Francis; Wong, Helen

doi:10.2140/agt.2017.17.3399

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Representations of the Kauffman bracket skein algebra, II: Punctured surfaces

Francis Bonahon and Helen Wong

Algebraic & Geometric Topology 17 (2017) 3399–3434

DOI: 10.2140/agt.2017.17.3399

Abstract

In part I, we constructed invariants of irreducible finite-dimensional representations of the Kauffman bracket skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation that realizes these invariants. The current article is restricted to surfaces with at least one puncture, a condition that is lifted in subsequent work relying on this one. A step in the proof is of independent interest, and describes the arithmetic structure of the Thurston intersection form on the space of integer weight systems for a train track.

Keywords

Kauffman bracket, skein algebra, quantum Teichmüller space

Mathematical Subject Classification 2010

Primary: 57M27, 57R56

Secondary: 57M27

References

Publication

Received: 8 March 2016

Revised: 27 September 2016

Accepted: 25 April 2017

Published: 4 October 2017

Authors

Francis Bonahon
Department of Mathematics University of Southern California Los Angeles, CA United States

Helen Wong
Department of Mathematics Carleton College Northfield, MN United States

Volume 17, issue 6 (2017)