Homeomorphisms f of a manifold M are recoverable from the marked isomorphism class of finitely generated groups of homeomorphisms containing f, with applications to critical regularity and differential rigidity of diffeomorphism groups on 1-manifolds.
Algebraic Structure of Diffeomorphism Groups of One-Manifolds
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abstract
It is a celebrated result of Mather that the group of $C^k$--diffeomorphisms of an $n$--manifold is simple, provided that a mild isotopy condition is satisfied, with the possible exception of $k=n+1$. The purpose of this article is mostly expository, and in it we give a detailed account of Mather's proof in the case when $n=1$.
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2019 1verdicts
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Reconstructing maps out of groups
Homeomorphisms f of a manifold M are recoverable from the marked isomorphism class of finitely generated groups of homeomorphisms containing f, with applications to critical regularity and differential rigidity of diffeomorphism groups on 1-manifolds.