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QUANTUM TEICHMÜLLER SPACES AND QUANTUM TRACE MAP

Part of: Low-dimensional topology Topological manifolds

Published online by Cambridge University Press:  06 April 2017

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

Keywords

Kauffman bracket skein modulequantum Teichmüller spacequantum trace map

MSC classification

Primary: 57N10: Topology of general $3$-manifolds 57M25: Knots and links in $S^3$
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 2 , March 2019 , pp. 249 - 291
Copyright
© Cambridge University Press 2017 

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Footnotes

Supported in part by National Science Foundation.

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