Recognition of -singularities of functions.
Using the description of non solvable dynamics by Nakai, we give in this paper a new proof of the rigidity properties of some sub-groups of Diff(C, O). The Cinfinity case is also considered here.
We introduce a 1-cocycle on the group of diffeomorphisms Diff(M) of a smooth manifold M endowed with a projective connection. This cocycle represents a nontrivial cohomology class of Diff(M) related to the Diff(M)-modules of second order linear differential operators on M. In the one-dimensional case, this cocycle coincides with the Schwarzian derivative, while, in the multi-dimensional case, it represents its natural and new generalization. This work is a continuation of [3] where the same problems...
We study the cohomology of the group consisting of all -diffeomorphisms of the line, which are -flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.
We prove that the space of orientation preserving homeomorphisms of the 2-sphere which fix pointwise a nontrivial nonseparating continuum is a contractible absolute neighborhood retract homeomorphic to the separable Hilbert space .
Il est démontré que le groupe des difféomorphismes du tore qui sont isotopes à l’identité est un groupe qui est égal à son groupe des commutateurs. Il résulte de D.A.B. Epstein que c’est un groupe simple. Un lemme fondamental est utilisé ; il donne la structure locale des orbites de certaines translations du tore ; ce lemme est une application du théorème des fonctions implicites de F. Sergeraert.