Day's fixed point theorem, Group cohomology and Quasi-isometric rigidity

2015/02/03 by Tullia Dymarz, Dymarz, Tullia, Xiangdong Xie +1
Mathematics · #20F65 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1502.00710

openalex publication_date 2015/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Isometry groups of Riemannian solvmanifolds
• Quasiconformal maps in metric spaces with controlled geometry

Related

• First cohomology, rigidity and deformations of isometric group actions
• Homology and dynamics in quasi-isometric rigidity of once-punctured mapping class groups
• Rigidity of groups of circle diffeomorphisms and Teichmüller spaces
• Quasi-isometry rigidity of groups
• Coarse fixed point properties