Displaying similar documents to “Factorizable groups of homeomorphisms”

On the first homology of automorphism groups of manifolds with geometric structures

Kōjun Abe, Kazuhiko Fukui (2005)

Open Mathematics

Similarity:

Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.

On the homeomorphism groups of manifolds and their universal coverings

Agnieszka Kowalik, Tomasz Rybicki (2011)

Open Mathematics

Similarity:

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.

The C 1 generic diffeomorphism has trivial centralizer

Christian Bonatti, Sylvain Crovisier, Amie Wilkinson (2009)

Publications Mathématiques de l'IHÉS

Similarity:

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.

On admissible groups of diffeomorphisms

Rybicki, Tomasz

Similarity:

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...

Orderable 3-manifold groups

Steven Boyer, Dale Rolfsen, Bert Wiest (2005)

Annales de l’institut Fourier

Similarity:

We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact P 2 -irreducible manifolds with positive first Betti number. For seven of the eight geometries (excluding hyperbolic) we are able to characterize which manifolds’ groups support a left-invariant or bi-invariant ordering. We also show that manifolds modelled on these geometries have virtually bi-orderable groups. The question...