## Algebraic & Geometric Topology

### Factorization rules in quantum Teichmüller theory

Julien Roger

#### Abstract

For a punctured surface $S$, a point of its Teichmüller space $T(S)$ determines an irreducible representation of its quantization $Tq(S)$. 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 $Tq(S)$ limits to a direct sum of representations of $Tq(Sγ)$, where $Sγ$ 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 13, Number 6 (2013), 3411-3446.

Dates
Received: 8 February 2013
Accepted: 19 April 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715737

Digital Object Identifier
doi:10.2140/agt.2013.13.3411

Mathematical Reviews number (MathSciNet)
MR3248738

Zentralblatt MATH identifier
1311.57024

#### Citation

Roger, Julien. Factorization rules in quantum Teichmüller theory. Algebr. Geom. Topol. 13 (2013), no. 6, 3411--3446. doi:10.2140/agt.2013.13.3411. https://projecteuclid.org/euclid.agt/1513715737

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