Fenchel-Nielsen coordinates on upper bounded pants decompositions

被引:6
|
作者
Saric, Dragomir [1 ,2 ]
机构
[1] CUNY Queens Coll, Dept Math, Flushing, NY 11367 USA
[2] CUNY, Grad Ctr, Math PhD Program, New York, NY 10016 USA
基金
美国国家科学基金会;
关键词
TEICHMULLER SPACE; SURFACES;
D O I
10.1017/S0305004114000656
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let X-0 be an infinite-type hyperbolic surface (whose boundary components, if any, are closed geodesics) which has an upper bounded pants decomposition. The length spectrum Teichmuller space T-ls(X-0) consists of all surfaces X homeomorphic to X-0 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 T-ls(X-0) and using these coordinates they proved that T-ls(X-0) is path connected. We use the Fenchel-Nielsen coordinates for T-ls(X-0) to induce a locally bi-Lipschitz homeomorphism between l(infinity) and Tls(X-0) (which extends analogous results by Fletcher [9] and by Allessandrini, Liu, Papadopoulos, Su and Sun [2] for the unreduced and the reduced T-qc(X-0)). Consequently, T-ls(X-0) is contractible. We also characterize the closure in the length spectrum metric of the quasiconformal Teichmuller space T-qc(X-0) in T-ls(X-0).
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页码:385 / 397
页数:13
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