Geodesic
Representations of the Kauffman bracket skein algebra, II: Punctured surfaces
Bonahon, Francis1 ; Wong, Helen2
1 Department of Mathematics, University of Southern California, Los Angeles, CA, United States
2 Department of Mathematics, Carleton College, Northfield, MN, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 6, pp. 3399-3434

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2017.17.3399
Classification : 57M27, 57R56, 57M27
Keywords: Kauffman bracket, skein algebra, quantum Teichmüller space

Bonahon, Francis 1 ; Wong, Helen 2

1 Department of Mathematics, University of Southern California, Los Angeles, CA, United States
2 Department of Mathematics, Carleton College, Northfield, MN, United States 
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Bonahon, Francis; Wong, Helen. Representations of the Kauffman bracket skein algebra, II: Punctured surfaces. Algebraic and Geometric Topology, Tome 17 (2017) no. 6, pp. 3399-3434. doi: 10.2140/agt.2017.17.3399

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