Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The notion of Cr,s and C∞,s-diffeomorphisms is introduced. It is shown that the identity component of the group of leaf preserving C∞,s-diffeomorphisms with compact supports is perfect. This result is a modification of the Mather and Epstein perfectness theorem.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
313--324
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- AGH University of Science and Technology Faculty of Applied Mathematics, al. Mickiewicza 30, 30-065 Cracow, Poland, lechjace@wms.mat.agh.edu.pl
Bibliografia
- [1] V.I. Arnold, Small denominators. I, Mappings of the circumference onto itself, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961) = Amer. Math. Soc. Translations ser 2. 46 (1965), 213–284.
- [2] D.B.A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math. 22 (1970), 165–173.
- [3] D.B.A. Epstein, Commutators of C∞-diffeomorphisms. Appendix to ’A curious remark concerning the geometric transfer map’ by John N. Mather, Comment. Math. Helv. 59 (1984), 111–122.
- [4] M.R. Herman, Sur le groupe des difféomorphismes du tore, Ann. Inst. Fourier, Grenoble 23 (1973) 2, 75–86.
- [5] J. Lech, T. Rybicki, Groups of Cr,s-diffeomorphisms related to a foliation, Geometry and Topology of Manifolds, Banach Center Publications, 76 (2007), 437–450.
- [6] J.N. Mather, Commutators of diffeomorphisms, Comment. Math. Helv. 49 (1974), 512–528.
- [7] J.N. Mather, Commutators of diffeomorphisms, II, Comment. Math. Helv. 50 (1975), 33–40.
- [8] J.N. Mather, A curious remark concerning the geometric transfer map, Comment. Math. Helv. 59 (1984), 86–110.
- [9] J.N. Mather, Commutators of diffeomorphisms, III: a group which is not perfect, Comment. Math. Helv. 60 (1985), 122–124.
- [10] T. Rybicki, The identity component of the leaf preserving diffeomorphism group is perfect, Monatsh. Math. 120 (1995), 289–305.
- [11] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 304–307.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH9-0004-0007