Algebraic & Geometric Topology

Factorization rules in quantum Teichmüller theory

Julien Roger

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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 (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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx] 20G42: Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]

quantum Teichmüller space Weil–Petersson geometry ideal triangulations shear coordinates


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

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