Smooth perfectness for the group of diffeomorphisms

Details Smooth perfectness for the group of diffeomorphisms Smooth perfectness for the group of diffeomorphisms

2004-09-30

arxiv.org/abs/math/0409605v3

Mathematics

Differential Geometry

Fully revised and extended second version of our paper math.DG/0409605 with improved results. Tomasz Rybicki contributed sub

Scientific paper

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 $g$.

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