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.
Keywords: quantum Teichmüller space, Weil–Petersson geometry, ideal triangulations, shear coordinates
Roger, Julien 1
@article{10_2140_agt_2013_13_3411,
author = {Roger, Julien},
title = {Factorization rules in quantum {Teichm\"uller} theory},
journal = {Algebraic and Geometric Topology},
pages = {3411--3446},
year = {2013},
volume = {13},
number = {6},
doi = {10.2140/agt.2013.13.3411},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.3411/}
}
Roger, Julien. Factorization rules in quantum Teichmüller theory. Algebraic and Geometric Topology, Tome 13 (2013) no. 6, pp. 3411-3446. doi: 10.2140/agt.2013.13.3411
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