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QUANTUM TEICHMÜLLER SPACES AND QUANTUM TRACE MAP

Published online by Cambridge University Press:  06 April 2017

Thang T. Q. Lê*
Affiliation:
School of Mathematics, 686 Cherry Street, Georgia Tech, Atlanta, GA 30332, USA ([email protected])

Abstract

We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum Teichmüller space of a marked surface, defined by Chekhov–Fock (and Kashaev) in an abstract way, can be realized as a concrete subalgebra of the skew field of the skein algebra.

Type
Research Article
Copyright
© Cambridge University Press 2017 

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Footnotes

Supported in part by National Science Foundation.

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