几何有限双曲流形的弯曲参数化
Bending parameterization of geometrically finite hyperbolic manifolds
- University of Luxembourg（卢森堡大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明非 Fuchs 型几何有限双曲结构由弯曲叶状结构唯一确定，弯曲映射为同胚，推广了凸余紧情形，并建立了边界纤维可收缩性判据。
AI中文摘要：
我们证明，在给定的可双曲化三维流形 M 上，非 Fuchs 型几何有限双曲结构在保向同痕意义下由其弯曲叶状结构唯一确定。因此，从赋予强拓扑的 M 上非 Fuchs 型几何有限结构空间到赋予 Lecuire 管状拓扑的弯曲叶状结构空间的弯曲映射是一个同胚。这推广了与 Schlenker 一起建立的凸余紧情形。证明结合了双曲 Dehn 填充、弯曲映射的连续性与真性（Lecuire）及其纤维的实解析性（Bonahon）。我们还建立了同胚连续延拓的边界纤维可收缩性判据，将 Finney 定理推广到边界情形。这一拓扑结果可能具有独立意义。
英文摘要：
We show that non-Fuchsian geometrically finite hyperbolic structures on a given hyperbolizable 3-manifold M are uniquely determined, up to isotopy, by their bending laminations. Consequently, the bending map from the space of non-Fuchsian geometrically finite structures on M, endowed with the strong topology, to the space of bending laminations, endowed with Lecuire's tubular topology, is a homeomorphism. This extends the convex co-compact case established with Schlenker. The proof combines hyperbolic Dehn filling, continuity and properness of the bending map (Lecuire) and real-analyticity of its fibres (Bonahon). We also establish a criterion for contractibility of the boundary fibres of a continuous extension of a homeomorphism, extending Finney's theorem to a boundary setting. This topological result may be of independent interest.
