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2017 Representations of the Kauffman bracket skein algebra, II: Punctured surfaces
Francis Bonahon, Helen Wong
Algebr. Geom. Topol. 17(6): 3399-3434 (2017). DOI: 10.2140/agt.2017.17.3399


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.


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Francis Bonahon. Helen Wong. "Representations of the Kauffman bracket skein algebra, II: Punctured surfaces." Algebr. Geom. Topol. 17 (6) 3399 - 3434, 2017.


Received: 8 March 2016; Revised: 27 September 2016; Accepted: 25 April 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06791652
MathSciNet: MR3709650
Digital Object Identifier: 10.2140/agt.2017.17.3399

Primary: 57M27, 57R56
Secondary: 57M27

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.17 • No. 6 • 2017
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