Embedding smooth and formal diffeomorphisms through the Jordan–Chevalley decomposition

Smooth Perfectness through Decomposition of Diffeomorphisms into Fiber Preserving Ones

We show that on a closed smooth manifold M equipped with k fiber bundle structures whose vertical distributions span the tangent bundle, every smooth diffeomorphism f of M sufficiently close to the identity can be written as a product f = f1 · · · fk, where fi preserves the ith-fiber. The factors fi can be chosen smoothly in f . We apply this result to show that on a certain class of closed smo...

Smooth Perfectness through Decomposition Ofdiffeomorphisms

Diffeomorphisms for Hilbert Manifolds and Handle Decomposition

1. We announce here the following result: Two homotopic diffeomorphisms of a paracompact separable Hubert manifold of infinite dimension are isotopic. (1) In this paper, a hilbert manifold (A-manifold) with or without boundary is always hausdorff, paracompact, separable C°°-differentiable and with the infinite dimensional separable hilbert space H as local model. Let M(M, dM) be an /^-manifold ...

Smooth Perfectness for the Group of Diffeomorphisms

Given the result of Herman, we provide a new elementary proof of the fact that the group of diffeomorphisms is a perfect and hence simple group. Moreover, we show that every diffeomorphism can be represented as a product of commutators f = [g1, h1] · · · [gm, hm] where the factors gi and hi can be chosen to depend smoothly on f . The elegance of our approach is due to the fact that we prove smo...

Non-commutative Hopf algebra of formal diffeomorphisms

The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the group law being multiplication of series, while the second group is the set of formal diffeomorphisms with the group law being composition of series. The motivation to introduce these Hopf algebras comes ...