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Hyperbolic metrics, measured foliations and pants decompositions for non-orientable surfaces

Papadopoulos, A. and Penner, R. C. (2016) Hyperbolic metrics, measured foliations and pants decompositions for non-orientable surfaces. Asian Journal of Mathematics, 20 (1). pp. 157-182. ISSN 1093-6106. doi:10.4310/AJM.2016.v20.n1.a7.

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We provide analogues for non-orientable surfaces with or without boundary or punctures of several basic theorems in the setting of the Thurston theory of surfaces which were developed so far only in the case of orientable surfaces. Namely, we provide natural analogues for non-orientable surfaces of the Fenchel–Nielsen theorem on the parametrization of the Teichmüller space of the surface, the Dehn–Thurston theorem on the parametrization of measured foliations in the surface, and the Hatcher–Thurston theorem, which gives a complete minimal set of moves between pair of pants decompositions of the surface. For the former two theorems, one in effect drops the twisting number for any curve in a pants decomposition which is 1-sided, and for the latter, two further elementary moves on pants decompositions are added to the two classical moves.

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Additional Information:© 2016 International Press of Boston, Inc. It is a pleasure for both authors to thank the Erwin Schrödinger Insitute for hosting and the GEometric structures And Representation varieties Network of the US National Science Foundation for partial support of an excellent trimester in Vienna when this work began. The first-named author was partially supported by the ANR French project ModGroup and the second- by QGM (Centre for the Quantum Geometry of Moduli Spaces) funded by the Danish National Research Foundation.
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Agence Nationale pour la Recherche (ANR)UNSPECIFIED
Danish National Research FoundationUNSPECIFIED
Subject Keywords:non-orientable surfaces, pants decompositions, Teichmüller space, Thurston’s boundary, Fenchel–Nielsen theorem, Dehn–Thurston theorem, Hatcher–Thurston theorem
Issue or Number:1
Classification Code:AMS Mathematics Subject Classification: 30F60, 32G15, 57M50, 57N16
Record Number:CaltechAUTHORS:20160317-104035382
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65427
Deposited By: Tony Diaz
Deposited On:17 Mar 2016 19:51
Last Modified:10 Nov 2021 23:45

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