Representations of the Kauffman bracket skein algebra II: punctured surfaces

Francis Bonahon; Helen Wong

doi:10.2140/agt.2017.17.3399

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arXiv · 1206.1639

Representations of the Kauffman bracket skein algebra II: punctured surfaces

Francis Bonahon·Helen Wong

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Abstract

In earlier work, we constructed invariants of irreducible representations of the Kauffman 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 will be lifted in subsequent work of the authors that relies on this one. A step in the proof is of independent interest, and describes the algebraic structure of the Thurston intersection form on the space of integer weight systems for a train track.

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BibTeX RIS

Francis Bonahon, Helen Wong. 2012-06-07. Representations of the Kauffman bracket skein algebra II: punctured surfaces. https://doi.org/10.2140/agt.2017.17.3399

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