Representations of the quantum Teichmuller space, and invariants of surface diffeomorphisms
Geometric Topology
2014-11-11 v5 Quantum Algebra
Abstract
We investigate the representation theory of the polynomial core 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 this polynomial core are classified, up to finitely many choices, by group homomorphisms from the fundamental group of the surface to the isometry group of the hyperbolic 3--space. We exploit this connection between algebra and hyperbolic geometry to exhibit new invariants of diffeomorphisms of S.
Keywords
Cite
@article{arxiv.math/0407086,
title = {Representations of the quantum Teichmuller space, and invariants of surface diffeomorphisms},
author = {Francis Bonahon and Xiaobo Liu},
journal= {arXiv preprint arXiv:math/0407086},
year = {2014}
}
Comments
Revised introduction. To appear in Geometry & Topology