The classification of punctured-torus groups.
The classification of punctured-torus groups.
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刺穿环面群的分类。
DOI：
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发表时间：
1998
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通讯作者：
Y. Minsky
中科院分区：
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作者：
Y. Minsky
瑟斯顿的最终叠层猜想提出，有限生成的克莱因群是由其商的拓扑和描述其末端渐近几何的不变量列表唯一确定的（直到等距）。我们针对穿孔环面群提出了这个猜想的证明。这些是具有抛物线换向器的自由双元克莱因群，应将其视为刺穿环面基本群的表示。因此，我们验证了刺穿环群变形空间的猜想拓扑描述（包括 Bers 的猜想，即该空间中的拟 Fuchsian 群是稠密的），并证明了一个刚性定理：两个刺穿环群是拟共形共轭的，当且仅当它们是拓扑共轭的。
Thurston’s ending lamination conjecture proposes that a flnitely generated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends. We present a proof of this conjecture for punctured-torus groups. These are free two-generator Kleinian groups with parabolic commutator, which should be thought of as representations of the fundamental group of a punctured torus. As a consequence we verify the conjectural topological description of the deformation space of punctured-torus groups (including Bers’ conjecture that the quasi-Fuchsian groups are dense in this space) and prove a rigidity theorem: two punctured-torus groups are quasi-conformally conjugate if and only if they are topologically conjugate.