Normal subgroups of diffeomorphism and homeomorphism groups of R^n and other open manifolds

Details Normal subgroups of diffeomorphism and homeomorphism groups of R^n and other open manifolds Normal subgroups of diffeomorphism and homeomorphism groups of R^n and other open manifolds

2009-11-25

arxiv.org/abs/0911.4835v3

Ergodic Theory and Dynamical Systems, 31 (2011), 1835-1847

Mathematics

Geometric Topology

This version corrects an error regarding the diffeomorphism groups of R^1, since the line has two ends, in contrast to higher

Scientific paper

10.1017/S0143385710000659

We determine all the normal subgroups of the group of C^r diffeomorphisms of R^n, r = 1,2,...,infinity, except when r=n+1 or n=4, and also of the group of homeomorphisms of R^n (r=0). We also study the group A_0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with nonempty boundary, then the quotient of A_0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

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