Factorization rules in quantum Teichmüller theory

Roger, Julien

doi:10.2140/agt.2013.13.3411

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Factorization rules in quantum Teichmüller theory

Julien Roger

Algebraic & Geometric Topology 13 (2013) 3411–3446

DOI: 10.2140/agt.2013.13.3411

Abstract

For a punctured surface $S$ , a point of its Teichmüller space $T (S)$ determines an irreducible representation of its quantization $T^{q} (S)$ . We analyze the behavior of these representations as one goes to infinity in $T (S)$ , or in the moduli space $ℳ (S)$ of the surface. The main result of this paper states that an irreducible representation of $T^{q} (S)$ limits to a direct sum of representations of $T^{q} (S_{γ})$ , where $S_{γ}$ is obtained from $S$ by pinching a multicurve $γ$ to a set of nodes. The result is analogous to the factorization rule found in conformal field theory.

Keywords

quantum Teichmüller space, Weil–Petersson geometry, ideal triangulations, shear coordinates

Mathematical Subject Classification 2010

Primary: 57M50

Secondary: 32G15, 20G42

References

Publication

Received: 8 February 2013

Accepted: 19 April 2013

Published: 10 October 2013

Authors

Julien Roger
Department of Mathematics Rutgers University 110 Frelinghuysen Rd Piscataway, NJ 08854-8019 USA
http://math.rutgers.edu/~juroger

Volume 13, issue 6 (2013)