End invariants and the classification of hyperbolic 3-manifolds
End invariants and the classification of hyperbolic 3-manifolds
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双曲 3 流形的末端不变量和分类
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
Y. Minsky
中科院分区：
文献类型：
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作者：
Y. Minsky
这些注记是对双曲3-流形和Kleinan群形变理论的一些最新发展的有偏见的指导。这个领域源于Poincaré和Klein的工作，通过瑟斯顿的几何化程序连接到拓扑学，通过Ahlfors-Bers拟共形理论进行分析，并通过瑟斯顿、Sullivan和其他人的工作连接到复杂动力学。它包含了许多技术和想法，对于一个单一的帐户来说，可能是一个太大的主题。我们将集中于双曲三维流形的末端和变形空间的边界的几何研究，特别是导致Brock，Canary和作者[82，23]最近解决瑟斯顿的“结束分层猜想”的不可压缩边界情况的技巧。研究了固定三维流形M上的双曲结构空间，将π1(M)的表示考虑到三维双曲空间H的等距群中，通过共轭达到自然等价.在这个空间里，被称为角色
These notes are a biased guide to some recent developments in the deformation theory of hyperbolic 3-manifolds and Kleinian groups. This field has its roots in the work of Poincaré and Klein, and connects to topology via Thurston’s geometrization program, to analysis via the Ahlfors-Bers quasiconformal theory, and to complex dynamics via the work of Thurston, Sullivan and others. It encompasses many techniques and ideas and may be too big a subject for a single account. We will focus on the geometric study of ends of hyperbolic 3-manifolds and boundaries of deformation spaces, and in particular on the techniques that led to the recent solution by Brock, Canary and the author [82, 23] of the incompressible-boundary case of Thurston’s “Ending Lamination Conjecture”. The space of hyperbolic structures on a fixed 3-manifold M is studied by considering representations of π1(M) into the isometry group of hyperbolic 3-space H, up to a natural equivalence by conjugation. In this space, called the character