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

top
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

top

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

top
  1. [1] A. Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Comment. Math. Helv. 53 (1978), 174-227. Zbl0393.58007
  2. [2] D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math. 22 (1970), 165-173. Zbl0205.28201
  3. [3] D. B. A. Epstein, Commutators of C ∞ -diffeomorphisms, Comment. Math. Helv. 59 (1984), 111-122. Zbl0535.58007
  4. [4] K. Fukui, Homologies of the group D i f f ∞ ( ℝ ⁿ , 0 ) and its subgroups, J. Math. Kyoto Univ. 20 (1980), 475-487. Zbl0476.57016
  5. [5] M. R. Herman, Sur le groupe des difféomorphismes du tore, Ann. Inst. Fourier (Grenoble) 23 (2) (1973), 75-86. 
  6. [6] A. Masson, Sur la perfection du groupe des difféomorphismes d'une variété à bord infiniment tangents à l'identité sur le bord, C. R. Acad. Sci. Paris Sér. A 285 (1977), 837-839. Zbl0409.58010
  7. [7] J. N. Mather, Commutators of diffeomorphisms, Comment. Math. Helv. I 49 (1974), 512-528; II 50 (1975), 33-40; III 60 (1985), 122-124. Zbl0289.57014
  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. 
  11. [11] F. Sergeraert, Feuilletages et difféomorphismes infiniment tangents à l'identité, Invent. Math. 39 (1977), 253-275. Zbl0327.58004
  12. [12] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 304-307. Zbl0295.57014

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.