Local representations of the quantum Teichmuller space

Abstract

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.

35 pages

References in corpus (2)

• Classical and quantum dilogarithmic invariants of flat PSL(2,C)-bundles over 3-manifolds
• Quantum Teichmüller spaces and Kashaev's 6j-symbols

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• Quantum coadjoint action and the $6j$-symbols of $U_{q}s{l}_2$
• Finite dimensional quantum Teichmüller space from the quantum torus at root of unity
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• Ptolemy groupoids, shear coordinates and the augmented Teichmuller space