Volume 10, issue 3 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Quantum traces in quantum Teichmüller theory

Christopher Hiatt

Algebraic & Geometric Topology 10 (2010) 1245–1283
Abstract

We prove that for the torus with one hole and p 1 punctures and the sphere with four holes there is a family of quantum trace functions in the quantum Teichmüller space, analog to the non-quantum trace functions in Teichmüller space, satisfying the properties proposed by Chekhov and Fock.

Keywords
Teichmüller, quantum, traces, skein relation, ideal triangulation, punctured torus, punctured sphere
Mathematical Subject Classification 2000
Primary: 81R05
References
Publication
Received: 17 December 2008
Accepted: 13 May 2009
Published: 1 June 2010
Authors
Christopher Hiatt
Department of Mathematics and Computer Science
University of Texas of the Permian Basin
Midland
Texas
USA