Superrigidity for irreducible lattices and geometric splitting
Superrigidity for irreducible lattices and geometric splitting
复制标题
不可约晶格和几何分裂的超刚性
DOI：
10.1090/s0894-0347-06-00525-x
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发表时间：
2005
影响因子：
3.9
通讯作者：
N. Monod
中科院分区：
文献类型：
--
作者：
N. Monod
我们证明了CAT（0）空间上不可约格作用的一般超刚性结果;首先，根据理想边界，然后针对内在几何（包括无限维空间）。特别地，我们得到了非单群中一致不可约格的Margulis超刚性定理的一个新的和完备的证明。证明依赖于简单的几何参数，包括一个分裂定理，它可以被视为劳森-丘/格罗莫尔-沃尔夫定理的无限维（和奇异）推广。附录A给出了一个非常基本的证明，附录B证明了我们的所有结果也适用于某些非均匀格。
We prove general superrigidity results for actions of irreducible lattices on CAT(0) spaces; first, in terms of the ideal boundary, and then for the intrinsic geometry (including for infinite-dimensional spaces). In particular, one obtains a new and self-contained proof of Margulis' superrigidity theorem for uniform irreducible lattices in non-simple groups. The proofs rely on simple geometric arguments, including a splitting theorem which can be viewed as an infinite-dimensional (and singular) generalization of the Lawson–Yau/Gromoll–Wolf theorem. Appendix A gives a very elementary proof of commensurator superrigidity; Appendix B proves that all our results also hold for certain non-uniform lattices.