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A Thurston boundary for infinite-dimensional Teichmüller spaces
Mathematische Annalen ( IF 1.3 ) Pub Date : 2021-02-09 , DOI: 10.1007/s00208-021-02148-z
Francis Bonahon , Dragomir Šarić

For a compact surface \(X_0\), Thurston introduced a compactification of its Teichmüller space \({\mathcal {T}}(X_0)\) by completing it with a boundary \(\mathcal {PML}(X_0)\) consisting of projective measured geodesic laminations. We introduce a similar bordification for the Teichmüller space \({\mathcal {T}}(X_0)\) of a noncompact Riemann surface \(X_0\), using the technical tool of geodesic currents. The lack of compactness requires the introduction of certain uniformity conditions which were unnecessary for compact surfaces. A technical step, providing a convergence result for earthquake paths in \({\mathcal {T}}(X_0)\), may be of independent interest.



中文翻译:

无限维Teichmüller空间的瑟斯顿边界

对于紧凑的表面\(X_0 \),瑟斯顿引入了边界\(\ mathcal {PML}(X_0)\),从而对其Teichmüller空间\({\ mathcal {T}}(X_0)\)进行了压缩。由测得的测地线叠层组成。我们使用测地线的技术工具为非紧致黎曼曲面\(X_0 \)的Teichmüller空间\ {{\ mathcal {T}}(X_0)\)引入了相似的化名。缺乏致密性需要引入某些均匀性条件,这对于致密表面而言是不必要的。为\({\ mathcal {T}}(X_0)\)中的地震路径提供收敛结果的技术步骤可能与您无关。

更新日期:2021-02-10
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