Smooth perfectness for the group of diffeomorphisms

Abstract

Given a result of Herman, we provide a new elementary proof of the fact that the connected component of the group of compactly supported diffeomorphisms is perfect and hence simple. Moreover, we show that every diffeomorphism $g$, which is sufficiently close to the identity, can be represented as a product of four commutators, $g=[h_1,k_1]\circ ...\circ [h_4,k_4]$, where the factors $h_i$ and $k_i$ can be chosen to depend smoothly on $g$.

Fully revised and extended second version of our paper math.DG/0409605 with improved results. Tomasz Rybicki contributed substantially to this second version and joined us as third author

Cited by in corpus (1)

• Lie Group Structures on Symmetry Groups of Principal Bundles