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

Paul A. Schweitzer S. J.

doi:10.1017/s0143385710000659

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arXiv · 0911.4835

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

Paul A. Schweitzer S. J.

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Abstract

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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BibTeX RIS

Paul A. Schweitzer S. J.. 2012-04-10. Normal subgroups of diffeomorphism and homeomorphism groups of R^n and other open manifolds. https://doi.org/10.1017/s0143385710000659

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