Factorization Rules in Quantum Teichmüller Theory

Abstract

We study the representation theory of the quantum Teichmueller space when going to infinity in the classical Teichmueller space. The geometric ingredients are the extension of Thurston's shear coordinates to the augmented Teichmueller space and the study of the Weil-Petersson Poisson structure for this extension. The result is analogous to the factorization rule found in conformal field theory.

28 pages, 7 figures. Version 2: corrected misprints, added Figure 3, corrected the proof of Proposition 9 and Lemma 19

References in corpus (5)

• The quantum dilogarithm and representations quantum cluster varieties
• An analog of a modular functor from quantized Teichm"uller theory
• Representations of the quantum Teichmuller space, and invariants of surface diffeomorphisms
• The Weil-Petersson metric geometry
• Local representations of the quantum Teichmuller space

Cited by in corpus (3)

• Density of $g$-vector cones from triangulated surfaces
• Ptolemy groupoids, shear coordinates and the augmented Teichmuller space
• A survey of quantum Teichmüller space and Kashaev algebra