Abstract
We investigate the representation theory of the polynomial core of the quantum Teichmüller space of a punctured surface . This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell decompositions of . Our main result is that irreducible finite-dimensional representations of are classified, up to finitely many choices, by group homomorphisms from the fundamental group to the isometry group of the hyperbolic 3–space . We exploit this connection between algebra and hyperbolic geometry to exhibit invariants of diffeomorphisms of .
Citation
Francis Bonahon. Xiaobo Liu. "Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms." Geom. Topol. 11 (2) 889 - 937, 2007. https://doi.org/10.2140/gt.2007.11.889
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