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GROUPS OF MEASURE-PRESERVING HOMEOMORPHISMS AS DEFORMATION RETRACTS

Published online by Cambridge University Press:  08 August 2003

RICARDO BERLANGA
RICARDO BERLANGA
Affiliation:
Instituto de Investigaciones en Matemáticas, Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, 04510 México DF, Méxicoberlanga@servidor.unam.mx
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Abstract

It is known that the group of homeomorphisms of a non-compact, connected, metrizable manifold acts transitively on certain spaces of measures defined, among other properties, by their behaviour at the manifold's set of ‘ends’. As a generalization of previous work of Fathi in the realm of compact manifolds, it is shown that the given action admits a continuous section when restricted to ‘biregular’ homeomorphisms and measures. This result exhibits the isotropy groups of measure-preserving homeomorphisms as deformation retracts of the corresponding acting groups.

Keywords

57S0558F11
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 241 - 254
Copyright
The London Mathematical Society 2003

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