On distortion in groups of homeomorphisms

Details On distortion in groups of homeomorphisms On distortion in groups of homeomorphisms

2011-11-06

arxiv.org/abs/1111.1449v1

J. Mod. Dyn. 5 (2011), no. 3, 609-622

Mathematics

Dynamical Systems

This paper mostly overlaps with part of arXiv:math/1105.0825. It is the version that is going to appear in print

Scientific paper

10.3934/jmd.2011.5.541

Let X be a path-connected topological space admitting a universal cover. Let Homeo(X,a) denote the group of homeomorphisms of X preserving degree one cohomology class a. We investigate the distortion in Homeo(X,a). Let g be an element of Homeo(X,a). We define a Nielsen-type equivalence relation on the space of g-invariant Borel probability measures on X and prove that if a homeomorphism g admits two nonequivalent invariant measures then it is undistorted. We also define a local rotation number of a homeomorphism generalising the notion of the rotation of a homeomorphism of the circle. Then we prove that a homeomorphism is undistorted if its rotation number is nonconstant.

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