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On the structure of certain nontransitive diffeomorphism groups on open manifolds

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that in some generic cases the identity component of the group of leaf preserving diffeomorphisms (with not necessarily compact support) on a foliated open manifold is perfect. Next, it is proved that it is also bounded, i.e. bounded with respect to any bi-invariant metric. It follows that the group is uniformly perfect as well.
Rocznik
Strony
511--520
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
autor
autor
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland, kowalik@wms.mat.agh.edu.pl
Bibliografia
  • [1] K. Abe, K. Fukui, Commutators of C1-diffeomorphisms preserving a submanifold, J. Math. Soc. Japan 61 (2009), 427–436.
  • [2] R.D. Anderson, On homeomorphisms as products of a given homeomorphism and its inverse, Topology of 3-manifolds, M. Fort (ed.), Prentice-Hall, 1961, 231–237.
  • [3] A. Banyaga, The structure of classical diffeomorphism groups, Mathematics and Its Applications, 400, Kluwer Academic Publishers Group, Dordrecht, 1997.
  • [4] D. Burago, S. Ivanov, L. Polterovich, Conjugation invariant norms on groups of geometric origin, Adv. Stud. Pure Math. 52, Groups of Diffeomorphisms (2008), 221–250.
  • [5] M.R. Herman, Sur le groupe des difféomorphismes du tore, Ann. Inst. Fourier (Grenoble) 23 (1973) 2, 75–86.
  • [6] M.W. Hirsch, Differential topology, Springer-Verlag, New York, 1976.
  • [7] J. Lech, T. Rybicki, Groups of Cr;s-diffeomorphisms related to a foliation, [in:] Geometry and Topology of Manifolds, Banach Center Publ. 76 (2007), 437–450.
  • [8] J.N. Mather, The vanishing of the homology of certain groups of homeomorphisms, Topology 10 (1971), 297–298.
  • [9] J.N. Mather, Commutators of diffeomorphisms, Comment. Math. Helv. 49 (1974), 512–528.
  • [10] J.N. Mather, Commutators of diffeomorphisms, II, Comment. Math. Helv. 50 (1975), 33–40.
  • [11] J.N. Mather, Commutators of diffeomorphisms, III: a group which is not perfect, Comment. Math. Helv. 60 (1985), 122–124.
  • [12] D. McDuff, The lattice of normal subgroups of the group of diffeomorphisms or homeomorphisms of an open manifold, J. London Math. Soc. 18 (1978), 353–364.
  • [13] T. Rybicki, The identity component of the leaf preserving diffeomorphism group is perfect, Monatsh. Math. 120 (1995), 289–305.
  • [14] T. Rybicki, On foliated, Poisson and Hamiltonian diffeomorphisms, Differential Geom. Appl. 15 (2001), 33–46.
  • [15] T. Rybicki, Boundedness of certain automorphism groups of an open manifold, Geom. Dedicata 151 (2011) 1, 175–186.
  • [16] P.A. Schweitzer, Normal subgroups of diffeomorphism and homeomorphism groups of Rn and other open manifolds, Ergodic Theory and Dynamical Systems, available on CJO, doi:10.1017/S0143385710000659.
  • [17] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 304–307.
  • [18] T. Tsuboi, On the group of foliation preserving diffeomorphisms, Foliations 2005, World Scientific, Singapore (2006), 411–430.
  • [19] T. Tsuboi, On the uniform perfectness of diffeomorphism groups, Adv. Stud. Pure Math. 52, Groups of Diffeomorphisms (2008), 505–524.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHS-0004-0008
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