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.
Cite this article
Tullia Dymarz, Xiangdong Xie, Day’s fixed point theorem, group cohomology and quasi-isometric rigidity. Groups Geom. Dyn. 10 (2016), no. 4, pp. 1121–1148DOI 10.4171/GGD/378