Displaying similar documents to “The simplicity of certain groups of homeomorphisms”

On the homeomorphism groups of manifolds and their universal coverings

Agnieszka Kowalik, Tomasz Rybicki (2011)

Open Mathematics

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Let H c(M) stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold M. It is shown that H c(M) is perfect and simple under mild assumptions on M. Next, conjugation-invariant norms on Hc(M) are considered and the boundedness of Hc(M) and its subgroups is investigated. Finally, the structure of the universal covering group of Hc(M) is studied.

On admissible groups of diffeomorphisms

Rybicki, Tomasz

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The phenomenon of determining a geometric structure on a manifold by the group of its automorphisms is a modern analogue of the basic ideas of the Erlangen Program of F. Klein. The author calls such diffeomorphism groups admissible and he describes them by imposing some axioms. The main result is the followingTheorem. Let ( M i , α i ) , i = 1 , 2 , be a geometric structure such that its group of automorphisms G ( M i , α i ) satisfies either axioms 1, 2, 3 and 4, or axioms 1, 2, 3’, 4, 5, 6 and 7, and M i is compact, or...

The C 1 generic diffeomorphism has trivial centralizer

Christian Bonatti, Sylvain Crovisier, Amie Wilkinson (2009)

Publications Mathématiques de l'IHÉS

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Answering a question of Smale, we prove that the space of C 1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.