Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms

By Francis Bonahon, Xiaobo Liu. 2004

60 citations recorded by the source corpus.

S of the quantum Teichmuller space of a punctured surface S . This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell decompositions of S . Our main result is that irreducible finite-dimensional representations of T q S are classified, up to finitely many choices, by group homomorphisms from the fundamental group 1.S/ to the isometry group of the hyperbolic 3‐space H 3 . We exploit this connection between algebra and hyperbolic geometry to exhibit invariants of diffeomorphisms of S . 57R56; 57M50, 20G42

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c0375e99e35f6414ab7fe14e53bab6c7eea2fc1d

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Representations of the Kauffman bracket skein algebra I: invariants and miraculous cancellations (2012, unknown): “The algebraic structure of the quantum Teichmüller space T (λ) is relatively simple, and its finite-dimensional irreducible representations are easily classified [3].”
Quantum traces for representations of surface groups in SL2(ℂ) (2010, methodology): “[5] Francis Bonahon, Xiaobo Liu, Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms, Geom.”
Unicity for representations of the Kauffman bracket skein algebra (2017, methodology): “One approach to this is via quantum Teichmüller theory [1,3,4].”