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Fenchel–Nielsen coordinates on upper bounded pants decompositions

Published online by Cambridge University Press:  16 January 2015

DRAGOMIR ŠARIĆ
DRAGOMIR ŠARIĆ*
Affiliation:
Department of Mathematics, Queens College of CUNY, 65-30 Kissena Blvd., Flushing, NY 11367, U.S.A. Mathematics PhD. Program, The CUNY Graduate Center, 365 Fifth Avenue, New York, NY 10016-4309, U.S.A. e-mail: [email protected]
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Abstract

Let X0 be an infinite-type hyperbolic surface (whose boundary components, if any, are closed geodesics) which has an upper bounded pants decomposition. The length spectrum Teichmüller space Tls(X0) consists of all surfaces X homeomorphic to X0 such that the ratios of the corresponding simple closed geodesics are uniformly bounded from below and from above. Alessandrini, Liu, Papadopoulos and Su [1] described the Fenchel–Nielsen coordinates for Tls(X0) and using these coordinates they proved that Tls(X0) is path connected. We use the Fenchel–Nielsen coordinates for Tls(X0) to induce a locally bi-Lipschitz homeomorphism between l∞ and Tls(X0) (which extends analogous results by Fletcher [9] and by Allessandrini, Liu, Papadopoulos, Su and Sun [2] for the unreduced and the reduced Tqc(X0)). Consequently, Tls(X0) is contractible. We also characterize the closure in the length spectrum metric of the quasiconformal Teichmüller space Tqc(X0) in Tls(X0).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 3 , May 2015 , pp. 385 - 397
Copyright
Copyright © Cambridge Philosophical Society 2015 

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References

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