Geometry & Topology
- Geom. Topol.
- Volume 11, Number 2 (2007), 889-937.
Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms
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 .
Geom. Topol., Volume 11, Number 2 (2007), 889-937.
Received: 16 December 2005
Accepted: 13 December 2006
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R56: Topological quantum field theories
Secondary: 57M50: Geometric structures on low-dimensional manifolds 20G42: Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
Bonahon, Francis; Liu, Xiaobo. Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms. Geom. Topol. 11 (2007), no. 2, 889--937. doi:10.2140/gt.2007.11.889. https://projecteuclid.org/euclid.gt/1513799864