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Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

Published online by Cambridge University Press:  12 January 2011

PAUL A. SCHWEITZER, S. J.
PAUL A. SCHWEITZER, S. J.*
Affiliation:
Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ 22453-900, Brazil (email: paul37sj@gmail.com)
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Abstract

We determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 6 , December 2011 , pp. 1835 - 1847
Copyright
Copyright © Cambridge University Press 2011

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