Superrigidity and mapping class groups
Superrigidity and mapping class groups
复制标题
超刚度和映射类组
DOI：
10.1016/s0040-9383(97)00099-2
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
H. Masur
中科院分区：
文献类型：
--
作者：
Benson Farb;H. Masur
Marguis的超刚性定理(见[22])指出，如果Γ是秩至少为2的实半单1李群G中的一个不可约格，则任何到单李群H的同态Γ→H都有有界象或扩张到同态G→H，并且当H是p-进群时象总是有界的。本文给出了两个非线性超刚性的例子：一个是关于映射类群和Teichmüler空间的，另一个是关于曲面的微分同胚群的。设S是一个紧的、可定向的、连通的、可能有边界的曲面。映射类群Mod(S)是S的保定向同胚类的同构类的群Homeo+(S)/Homeo0(S)。第一个结果的证明直接来自Kazhdan-Marguis和Kaimanovich-Masur的定理，以及Mod(S)的一些结构理论。
Margulis’s superrigidity theorem (see [22]) says that if Γ is an irreducible lattice in a real semisimple 1 Lie group G of rank at least two, then any homomorphism Γ→ H into a simple Lie group H has bounded image or extends to a homomorphism G→ H, and the image is always bounded when H is a p-adic group. In this note we give two examples of nonlinear superrigidity: one for mapping class groups and Teichmüller space, another for diffeomorphism groups of surfaces.Let S be a compact, orientable, connected surface, possibly with boundary. The mapping class group Mod (S) is the group Homeo+(S)/Homeo 0 (S) of isotopy classes of orientation-preserving homeomorphisms of S. The proof of our first result will come directly from theorems of Kazhdan–Margulis and Kaimanovich–Masur, together with some structure theory of Mod (S).