Large scale geometry of homeomorphism groups

Kathryn Mann; Christian Rosendal

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arXiv · 1607.02106

Large scale geometry of homeomorphism groups

Kathryn Mann·Christian Rosendal

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Abstract

Let M be a compact manifold. We show the identity component $\mathrm{Homeo}_0(M)$ 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.

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Kathryn Mann, Christian Rosendal. 2016-07-07. Large scale geometry of homeomorphism groups. https://arxiv.org/abs/1607.02106

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