Groups, Geometry, and Dynamics


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Volume 10, Issue 4, 2016, pp. 1121–1148
DOI: 10.4171/GGD/378

Published online: 2017-01-26

Day’s fixed point theorem, group cohomology and quasi-isometric rigidity

Tullia Dymarz[1] 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