Representations of the Kauffman bracket skein algebra II: punctured surfaces
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.
Keywords
Cite
@article{arxiv.1206.1639,
title = {Representations of the Kauffman bracket skein algebra II: punctured surfaces},
author = {Francis Bonahon and Helen Wong},
journal= {arXiv preprint arXiv:1206.1639},
year = {2018}
}
Comments
22 pages. Version 2: The article was much reorganized, for compatibility with the subsequent article [BonWon6] in the same series; the results are unchanged. Version 3: This new version takes into account the possible impact of sign reversal symmetries, overlooked in the earlier versions, on the uniqueness properties needed for [BonWon6]; the manuscript is now ready for journal submission