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2011 | 9 | 6 | 1217-1231
Tytuł artykułu

On the homeomorphism groups of manifolds and their universal coverings

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let H c(M) stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold M. It is shown that H c(M) is perfect and simple under mild assumptions on M. Next, conjugation-invariant norms on Hc(M) are considered and the boundedness of Hc(M) and its subgroups is investigated. Finally, the structure of the universal covering group of Hc(M) is studied.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
6
Strony
1217-1231
Opis fizyczny
Daty
wydano
2011-12-01
online
2011-09-23
Twórcy
Bibliografia
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  • [5] Brown K.S, Cohomology of Groups, Grad. Texts in Math., 87, Springer, New York-Heidelberg-Berlin, 1982
  • [6] Burago D., Ivanov S., Polterovich S., Conjugation-invariant norms on groups of geometric origin, In: Groups of Diffeomorphisms, Adv. Stud. Pure Math., 52, Math. Soc. Japan, Tokyo, 2008, 221–250
  • [7] Edwards R.D., Kirby R.C., Deformations of spaces of imbeddings, Ann. of Math., 1971, 93, 63–88 http://dx.doi.org/10.2307/1970753
  • [8] Fisher G.M., On the group of all homeomorphisms of a manifolds, Trans. Amer. Math. Soc., 1960, 97, 193–212 http://dx.doi.org/10.1090/S0002-9947-1960-0117712-9
  • [9] Fukui K., Homologies of the group Diff∞(ℝn, 0) and its subgroups, J. Math. Kyoto Univ., 1980, 20(3), 475–487
  • [10] Fukui K., Imanishi H., On commutators of foliation preserving homeomorphisms, J. Math. Soc. Japan, 1999, 51(1), 227–236 http://dx.doi.org/10.2969/jmsj/05110227
  • [11] Haller S., Rybicki T., On the group of diffeomorphisms preserving a locally conformal symplectic structure, Ann. Global Anal. Geom., 1999, 17(5), 475–502 http://dx.doi.org/10.1023/A:1006650124434
  • [12] Hirsch M.W., Differential Topology, Grad. Texts in Math., 33, Springer, New York-Heidelberg, 1976
  • [13] Ling W., Factorizable groups of homeomorphisms, Compositio Math., 1984, 51(1), 41–50
  • [14] Mather J.N., The vanishing of the homology of certain groups of homeomorphisms, Topology, 1971, 10(4), 297–298 http://dx.doi.org/10.1016/0040-9383(71)90022-X
  • [15] Mather J.N., Commutators of diffeomorphisms. I, II, Comment. Math. Helv., 1974, 49, 512–528; 1975, 50, 33–40 http://dx.doi.org/10.1007/BF02566746
  • [16] McDuff D., The lattice of normal subgroups of the group of diffeomorphisms or homeomorphisms of an open manifold, J. Lond. Math. Soc., 1978, 18(2), 353–364 http://dx.doi.org/10.1112/jlms/s2-18.2.353
  • [17] Rybicki T., Commutators of diffeomorphisms of a manifold with boundary, Ann. Polon. Math., 1998, 68(3), 199–210
  • [18] Rybicki T., On commutators of equivariant homeomorphisms, Topology Appl., 2007, 154(8), 1561–1564 http://dx.doi.org/10.1016/j.topol.2006.12.003
  • [19] Rybicki T., Commutators of contactomorphisms, Adv. Math., 2010, 225(6), 3291–3326 http://dx.doi.org/10.1016/j.aim.2010.06.004
  • [20] Rybicki T., Boundedness of certain automorphism groups of an open manifold, Geom. Dedicata, 2011, 151(1), 175–186 http://dx.doi.org/10.1007/s10711-010-9525-4
  • [21] Rybicki T., Locally continuously perfect groups of homeomorphisms, Ann. Global Anal. Geom., 2011, 40(2), 191–202 http://dx.doi.org/10.1007/s10455-011-9253-5
  • [22] Siebenmann L.C., Deformation of homeomorphisms on stratified sets. I, II, Comment. Math. Helv., 1972, 47, 123–136, 137–163 http://dx.doi.org/10.1007/BF02566793
  • [23] Thurston W., Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc., 1974, 80(2), 304–307 http://dx.doi.org/10.1090/S0002-9904-1974-13475-0
  • [24] Tsuboi T., On the homology of classifying spaces for foliated products, In: Foliations, Tokyo, 1983, Adv. Stud. Pure Math., 5, North-Holland, Amsterdam, 1985, 37–120
  • [25] Tsuboi T., On the perfectness of groups of diffeomorphisms of the interval tangent to the identity at the endpoints, In: Foliations: Geometry and Dynamics, Warsaw, 2000, World Scientific, River Edge, 2002, 421–440 http://dx.doi.org/10.1142/9789812778246_0022
  • [26] Tsuboi T., On the uniform perfectness of diffeomorphism groups, In: Groups of Diffeomorphisms, Adv. Stud. Pure Math., 52, Math. Soc. Japan, Tokyo, 2008, 505–524
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0081-4
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