Large scale geometry of homeomorphism groups

2016/07/07 by Mann, Kathryn, Rosendal, Christian · 4 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1607.02106

Abstract

Let M be a compact manifold. We show the identity component Homeo₀(M) of the group of self-homeomorphisms of M has a well-defined quasi-isometry type, and study its large scale geometry. Through examples, we relate this large scale geometry to both the topology of M and the dynamics of group actions on M. This gives a rich family of examples of non-locally compact groups to which one can apply the large-scale methods developed in previous work of the second author.

Cited by

• Coarse geometry of homeomorphism groups: Classifying countable Stone spaces
• Epimorphism classes and relatively maximal metrics in large-scale geometry
• Strongly bounded generation in transformation groups
• The infinite dimensional geometry of conjugation invariant generating sets

Related

• Actions of groups of homeomorphisms on one-manifolds
• Structure theorems for actions of homeomorphism groups
• On quasimorphisms and distortion in homeomorphism groups
• Large scale geometry of metrisable groups
• Locally approximating groups of homeomorphisms of manifolds