Groups, Geometry, and Dynamics
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Published online: 2017-01-26
Day’s fixed point theorem, group cohomology and quasi-isometric rigidityTullia Dymarz and Xiangdong Xie (1) University of Wisconsin, Madison, USA
In this note we explain how Day’s fixed point theorem can be used to conjugate certain groups of biLipschitz maps of a metric space into special subgroups like similarity groups. In particular, we use Day’s theorem to establish Tukia-type theorems and to give new proofs of quasi-isometric rigidity results.
Keywords: Day’s fixed point theorem, Tukia theorem, quasiconformal group, uniform quasisimilarity group
Dymarz Tullia, Xie Xiangdong: Day’s fixed point theorem, group cohomology and quasi-isometric rigidity. Groups Geom. Dyn. 10 (2016), 1121-1148. doi: 10.4171/GGD/378