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Locally continuously perfect groups of homeomorphisms

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Abstract

The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group of all homeomorphisms of a manifold is locally continuously perfect. The case of equivariant homeomorphism group and other examples are also considered.

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References

  1. Abe K., Fukui K.: On the structure of the group of Lipschitz homeomorphisms and its subgroups. J. Math. Soc. Japan 53, 501–511 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Banyaga A.: The structure of classical diffeomorphism groups, Mathematics and its Applications, 400. Kluwer Academic Publishers Group, Dordrecht (1997)

    Google Scholar 

  3. Bredon G.E.: Introduction to compact transformation groups. Academic Press, New York (1972)

    MATH  Google Scholar 

  4. Burago D., Ivanov S., Polterovich L.P.: Conjugation invariant norms on groups of geometric origin. Adv. Stud. Pure Math. 52, 221–250 (2008)

    MathSciNet  Google Scholar 

  5. Edwards R.D., Kirby R.C.: Deformations of spaces of imbeddings. Ann. Math. 93, 63–88 (1971)

    Article  MathSciNet  Google Scholar 

  6. Fisher G.M.: On the group of all homeomorphisms of a manifold. Trans. Amer. Math. Soc. 97, 193–212 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  7. Haller S., Teichmann J.: Smooth Perfectness through decomposition of diffeomorphisms into fiber preserving ones. Ann. Glob. Anal. Geom. 23, 53–63 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Herman M.R.: Sur le groupe des difféomorphismes du tore. Ann. Inst. Fourier (Grenoble) 23, 75–86 (1973)

    MATH  MathSciNet  Google Scholar 

  9. Hirsch M.W.: Differential Topology, Graduate Texts in Mathemetics 33. Springer, New York (1976)

    Google Scholar 

  10. Kriegl A., Michor P.W.: The Convenient Setting of Global Analysis, Mathematical Surveys and Monographs. Vol. 53. American Mathematical Society, USA (1997)

    Google Scholar 

  11. Lech J., Rybicki T.: Groups of C r,s-diffeomorphisms related to a foliation. Banach Center Publ 76, 437–450 (2007)

    Article  MathSciNet  Google Scholar 

  12. Ling W.: Factorizable groups of homeomorphisms. Compositio Math. 51(1), 41–50 (1984)

    MATH  MathSciNet  Google Scholar 

  13. Mather J.N.: The vanishing of the homology of certain groups of homeomorphisms. Topology 10, 297–298 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mather J.N.: Commutators of diffeomorphisms. Comment. Math. Helv. I 49, 512–528 (1974)

    Article  MathSciNet  Google Scholar 

  15. Mather J.N.: Commutators of diffeomorphisms. Comment. Math. Helv. II 50, 33–40 (1975)

    Article  MathSciNet  Google Scholar 

  16. Mather J.N.: Commutators of diffeomorphisms. Comment. Math. Helv. III 60, 122–124 (1985)

    Article  MathSciNet  Google Scholar 

  17. Rybicki T.: The identity component of the leaf preserving diffeomorphism group is perfect. Monatsh. Math. 120, 289–305 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  18. Rybicki, T.: Commutators of C r-diffeomorphisms acting along leaves. Proceedings of the Conference “Differential Geometry and Applications” pp. 299–307, Masaryk University, August 1995, Brno 1996

  19. Rybicki T.: On commutators of equivariant homeomorphisms. Topology Appl. 154, 1561–1564 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Rybicki T.: Commutators of contactomorphisms. Adv. Math. 225, 3291–3326 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  21. Rybicki, T.: Boundedness of certain automorphism groups of an open manifold. Geometriae Dedicata (in press), available at arXiv 0912.4590v3

  22. Siebenmann L.C.: Deformation of homeomorphisms on stratified sets I, II. Comment. Math. Helv. 47, 123–163 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  23. Thurston W.: Foliations and groups of diffeomorphisms. Bull. Amer. Math. Soc. 80, 304–307 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  24. Tsuboi T.: On the homology of classifying spaces for foliated products. Adv. Stud. Pure Math. 5, 37–120 (1985)

    MathSciNet  Google Scholar 

  25. Tsuboi T.: On the uniform perfectness of diffeomorphism groups. Adv. Stud. Pure Math. 52, 505–524 (2008)

    MathSciNet  Google Scholar 

  26. Tsuboi T.: On the group of real analytic diffeomorphisms. Ann. Sci. Éc. Norm. Supér 42(4), 601–651 (2009)

    MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Applied Mathematics, AGH University of Science and Technology, Al., Mickiewicza 30, 30-059, Kraków, Poland

    Tomasz Rybicki

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  1. Tomasz Rybicki
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Correspondence to Tomasz Rybicki.

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Rybicki, T. Locally continuously perfect groups of homeomorphisms. Ann Glob Anal Geom 40, 191–202 (2011). https://doi.org/10.1007/s10455-011-9253-5

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  • DOI: https://doi.org/10.1007/s10455-011-9253-5

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