Local representations of the quantum Teichmuller space

Details Local representations of the quantum Teichmuller space Local representations of the quantum Teichmuller space

2007-07-14

arxiv.org/abs/0707.2151v1

Mathematics

Geometric Topology

35 pages

Scientific paper

We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choices, these purely algebraic representations are classified by classical geometric data. We also investigate the family of intertwining operators associated to such a representations. In particular, we use these intertwiners to construct a natural fiber bundle over the Teichmuller space and its quotient under the action of the mapping class group. This construction also offers a convenient framework to exhibit invariants of surface diffeomorphisms.

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