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Representations of the
Kauffman bracket skein algebra, II: Punctured surfaces
Francis Bonahon and Helen Wong |
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Algebraic & Geometric Topology 17 (2017) 3399–3434
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Abstract |
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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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Keywords
Kauffman bracket, skein algebra, quantum Teichmüller space
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Mathematical Subject Classification 2010
Primary: 57M27, 57R56
Secondary: 57M27
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References |
Publication
Received: 8 March 2016
Revised: 27 September 2016
Accepted: 25 April 2017
Published: 4 October 2017
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Authors |
| Francis Bonahon | |
| Department of Mathematics University of Southern California Los Angeles, CA United States |
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| Helen Wong | |
| Department of Mathematics Carleton College Northfield, MN United States |
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