Ideal bicombings for hyperbolic groups and applications
群论
2012-07-10 v2 度量几何
摘要
For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established by Monod-Shalom hold for all non-elementary hyperbolic groups and their non-elementary subgroups. We also derive superrigidity results for actions of general irreducible lattices on a large class of hyperbolic metric spaces.
引用
@article{arxiv.math/0304278,
title = {Ideal bicombings for hyperbolic groups and applications},
author = {I. Mineyev and N. Monod and Y. Shalom},
journal= {arXiv preprint arXiv:math/0304278},
year = {2012}
}
备注
Substantial generalizeation; now the results hold for a general class of hyperbolic metric spaces (rather than just hyperbolic groups)