Fenchel–Nielsen coordinates on upper bounded pants decompositions
Fenchel–Nielsen coordinates on upper bounded pants decompositions
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DOI：
10.1017/s0305004114000656
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发表时间：
2012-09
影响因子：
0.8
通讯作者：
D. Šarić
中科院分区：
文献类型：
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作者：
D. Šarić
摘要设X0是一个具有上界裤子分解的无限型双曲曲面（其边界分量为封闭测地线）。长度谱teichm<s:1> ller空间Tls（X0）由与X0同胚的所有曲面X组成，使得对应的简单封闭测地线的比值从下到上均匀有界。Alessandrini, Liu， Papadopoulos和Su[1]描述了tl （X0）的fenchell - nielsen坐标，并利用这些坐标证明了tl （X0）是路径连通的。我们利用tl （X0）的fenchell - nielsen坐标推导出tl （X0）与l∞之间的局部bi-Lipschitz同纯（推广了Fletcher[9]和Allessandrini， Liu, Papadopoulos， Su和Sun[2]对于未约化和约化Tqc（X0）的类似结果）。因此，Tls（X0）是可收缩的。我们还描述了tls0 （X0）中拟共形teichm<s:1>空间Tqc（X0）的长度谱度量中的闭包性。
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).