Smooth perfectness for the group of diffeomorphisms

Stefan Haller; Tomasz Rybicki; Josef Teichmann

Smooth perfectness for the group of diffeomorphisms

Differential Geometry 2012-01-12 v3

Authors: Stefan Haller , Tomasz Rybicki , Josef Teichmann

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 $g$ .

Keywords

diffeomorphism groups smooth 4-manifolds group theory

Cite

@article{arxiv.math/0409605,
  title  = {Smooth perfectness for the group of diffeomorphisms},
  author = {Stefan Haller and Tomasz Rybicki and Josef Teichmann},
  journal= {arXiv preprint arXiv:math/0409605},
  year   = {2012}
}

Comments

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

Smooth perfectness for the group of diffeomorphisms

Abstract

Keywords

Cite

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