Commutators of diffeomorphisms of a manifold with boundary

Tomasz Rybicki

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 3, page 199-210
  • ISSN: 0066-2216

Abstract

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A well known theorem of Herman-Thurston states that the identity component of the group of diffeomorphisms of a boundaryless manifold is perfect and simple. We generalize this result to manifolds with boundary. Remarks on C r -diffeomorphisms are included.

How to cite

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Tomasz Rybicki. "Commutators of diffeomorphisms of a manifold with boundary." Annales Polonici Mathematici 68.3 (1998): 199-210. <http://eudml.org/doc/270572>.

@article{TomaszRybicki1998,
abstract = {A well known theorem of Herman-Thurston states that the identity component of the group of diffeomorphisms of a boundaryless manifold is perfect and simple. We generalize this result to manifolds with boundary. Remarks on $C^r$-diffeomorphisms are included.},
author = {Tomasz Rybicki},
journal = {Annales Polonici Mathematici},
keywords = {Group of diffeomorphisms; simplicity; perfectness; manifold with boundary; fixed point theory; group of diffeomorphisms of a smooth manifold},
language = {eng},
number = {3},
pages = {199-210},
title = {Commutators of diffeomorphisms of a manifold with boundary},
url = {http://eudml.org/doc/270572},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Tomasz Rybicki
TI - Commutators of diffeomorphisms of a manifold with boundary
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 3
SP - 199
EP - 210
AB - A well known theorem of Herman-Thurston states that the identity component of the group of diffeomorphisms of a boundaryless manifold is perfect and simple. We generalize this result to manifolds with boundary. Remarks on $C^r$-diffeomorphisms are included.
LA - eng
KW - Group of diffeomorphisms; simplicity; perfectness; manifold with boundary; fixed point theory; group of diffeomorphisms of a smooth manifold
UR - http://eudml.org/doc/270572
ER -

References

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  8. [8] J. Palis and S. Smale, Structural stability theorems, in: Proc. Sympos. Pure Math. 14, Amer. Math. Soc., 1970, 223-231. Zbl0214.50702
  9. [9] T. Rybicki, The identity component of the leaf preserving diffeomorphism group is perfect, Monatsh. Math. 120 (1995), 289-305. Zbl0847.57033
  10. [10] L. Schwartz, Analyse Mathématique, Hermann, Paris 1967. 
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  12. [12] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 304-307. Zbl0295.57014

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