Diffeomorphism groups of a manifold with boundary

  • Tomasz Rybicki
Part of the Mathematics and Its Applications book series (MAIA, volume 350)


It is observed that the identity component of some diffeomorphism groups on a manifold with boundary is perfect. We show also that a theorem of Filipkiewicz still holds in case of a manifold with boundary, that is, that the group of all diffeomorphisms on a manifold with boundary defines uniquely the topological and smooth structure of the manifold itself.

AMS classification



manifold with boundary diffeomorphism group perfect group isomorphism of groups inner automorphism 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Banyaga: On isomorphic classical diffeomorphism groups, II, J.Diff. Geo. 28 (1988), 23–35.MathSciNetzbMATHGoogle Scholar
  2. 2.
    A. Banyaga, R. de la Llave, C.E. Wayne: Cohomology equations and commutators of germs of contact diffeomorphisms, Trans. Amer. Math. Soc. 312 (1989), 755–778.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    D.B.A. Epstein: Commutators of C -diffeomorphisms, Comment. Math. Helv. 59 (1984), 111–122.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    R.P. Filipkiewicz: Isomorphisms between diffeomorphism groups, Ergodic. Th. & Dynam. Sys. 2 (1982), 159–171.MathSciNetzbMATHGoogle Scholar
  5. 5.
    K. Fukui: Homologies of the group Diff (Rn, 0) and its subgroups, J. Math. Kyoto Univ. 20(1980), 475–487.MathSciNetzbMATHGoogle Scholar
  6. 6.
    M. Golubitsky, V. Guillemin: Stable mappings and their singularities, Springer-Verlag, New York 1973.zbMATHGoogle Scholar
  7. 7.
    A. Masson: Sur la perfection du groupe des diffeomorphismes d’une variete a bord infinitement tangents a Videntite sur le bord, C. R. Acad. Sci. Paris Serie A 285(1977), 837–839.MathSciNetzbMATHGoogle Scholar
  8. 8.
    J.N. Mather: Commutators of diffeomorphisms, Comment. Math. Helv. I 49(1974), 512–528; II 50(1975), 33-40; III 60(1985), 122-124.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    J. Palis, S. Smale: Structural stability theorems, Proc.Symp. in Pure Math. 14, Amer.Math.Soc. 1970, 223-231.Google Scholar
  10. 10.
    T. Rybicki: Isomorphisms between groups of diffeomorphisms, Proc. Amer. Math. Soc. 123(1995), 303–310.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    T.Rybicki: On nontransitive groups of diffeomorphisms, preprint.Google Scholar
  12. 12.
    T.Rybicki: The identity component of the leaf preserving diffeomorphism group is perfect, to appear in Mh. Math. (1995).Google Scholar
  13. 13.
    F. Sergeraert: Feuilletages et diffeomorphismes infinitement tangents a Videntite, Invent. Math. 39(1977), 253–275.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    J.V. Whittaker: On isomorphic groups and homeomorphic spaces, Ann. of Math. 78(1963), 74–91.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Tomasz Rybicki
    • 1
  1. 1.Institute of MathematicsPedagogical UniversityRzeszówPoland

Personalised recommendations