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On distortion in groups of homeomorphisms

Publikationsart Peer-reviewed
Publikationsform Originalbeitrag (peer-reviewed)
Publikationsdatum 2011
Projekt Groupes sofiques: algèbre, analyse et dynamique
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Originalbeitrag (peer-reviewed)

Zeitschrift Journal of Modern Dynamics
Volume (Issue) 5(3)
Seite(n) 609 - 622
Titel der Proceedings Journal of Modern Dynamics

Abstract

Let X be a path-connected topological space admitting a universal cover. Let Homeo(X; a) denote the group of homeomorphisms of X preserving a degree one coho- mology class a. We investigate the distortion in Homeo(X; a). Let g 2 Homeo(X; a). We de ne a Nielsen-type equivalence relation on the space of g-invariant Borel proba- bility measures on X and prove that if a homeomorphism g admits two nonequivalent invariant measures then it is undistorted. We also de ne a local rotation number of a homeomorphism generalizing 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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