On the perfectness of C∞ s-diffeomorphism groups on a foliated manifold

• Autorzy: Lech J.
• Języki publikacji: EN

Abstrakty

EN

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

EN

group of C∞-diffeomorphisms; perfectness; commutator; foliation

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2008
• Tom: Vol. 28, no. 3
• Strony: 313--324
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Lech J.

• AGH University of Science and Technology Faculty of Applied Mathematics, al. Mickiewicza 30, 30-065 Cracow, Poland,

Bibliografia

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• [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.