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arXiv · 0901.1002

Uniform approximation of homeomorphisms by diffeomorphisms

Stefan Müller
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Abstract

We prove that a compactly supported homeomorphism of a smooth manifold of dimension greater or equal to 5 can be approximated uniformly by compactly supported diffeomorphisms if and only if it is isotopic to a diffeomorphism. If the given homeomorphism is in addition volume preserving, then it can be approximated uniformly by volume preserving diffeomorphisms.

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Stefan Müller. 2009-01-08. Uniform approximation of homeomorphisms by diffeomorphisms. https://doi.org/10.1016/j.topol.2014.10.003

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