Commentarii Mathematici Helvetici

, Volume 58, Issue 1, pp 48–71 | Cite as

Acyclic groups of automorphisms

  • Pierre de la Harpe
  • Dusa McDuff
Article
  • 36 Downloads

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AnS.
    J. H. Anderson andJ. G. Stampfli,Commutators and compressions, Israel J. Math.10 (1971) 433–441.MathSciNetGoogle Scholar
  2. And.
    R. D. Anderson,On homeomorphisms as products of conjugates of a given homeomorphism and its inverse. In “Topology of 3-manifolds and related topics”, M. K. Fort ed. (Prentice Hall 1962) 231–234.Google Scholar
  3. AS.
    H. Araki, M. Smith andL. Smith,On the homotopical significance of the type of von Neumann algebra factors, Commun. math. Phys.22 (1971) 71–88.CrossRefMathSciNetGoogle Scholar
  4. B.
    R. Baer,Die Kompositionsreihe der Gruppe aller eineindeutigen Abbildungen einer unendlichen Menge auf sich, Studia Math.5 (1935) 15–17.Google Scholar
  5. Bab.
    A. Babakhanian,Cohomological methods in group theory, Dekker 1972.Google Scholar
  6. Be.
    A. J. Berrick,An approach to algebraic K-theory, Pitman 1982.Google Scholar
  7. BDH.
    G. Baumslag, E. Dyer andA. Heller,The topology of discrete groups, J. Pure and Appl. Alg.16 (1980) 1–47.CrossRefMathSciNetGoogle Scholar
  8. BDM.
    G. Baumslag, E. Dyer andC. F. Miller,On the integral homology of finitely presented groups, Bull. Amer. Math. Soc.4 (1981) 321–324.MathSciNetGoogle Scholar
  9. Br.
    M. Breuer,A homotopy theoretic proof of the additivity of the trace, Rocky Math. J.10 (1980) 185–198. (Section 4 has to be corrected, but theorem 5 is correct as such.)MathSciNetGoogle Scholar
  10. BP.
    A. Brown andC. Pearcy,Structure of commutators of operators, Ann. of Math.82 (1965) 112–127.CrossRefMathSciNetGoogle Scholar
  11. BHS.
    L. G. Brown, P. de la Harpe andC. Schochet,Perfection du groupe de Fredholm, C.R. Acad. Sci. Paris, Sér. A,290 (1980) 151–154.Google Scholar
  12. BW.
    J. Brüning andW. Willgerodt,Ein Verallgemeinerung eines Satzes von N. Kuiper, Math. Ann220 (1976) 47–58.CrossRefMathSciNetGoogle Scholar
  13. DD.
    J. Dixmer andA. Douady,Champs continus d’espaces hilbertiens et de C * -algèbres, Bull. Soc. Math. France91 (1963) 227–284.MathSciNetGoogle Scholar
  14. D.
    A. Douady,Un espace de Banach dont le groupe linéaire n’est pas connexe, indag. Math.27 (1965) 787–789.MathSciNetGoogle Scholar
  15. Ei.
    S. J. Eigen,On the simplicity of the full group of ergodic transformations, Israel J. Math.40 (1981) 345–349.MathSciNetGoogle Scholar
  16. Ep.
    D. B. A. Epstein,The simplicity of certain groups of homeomorphisms, Compositio Math.22 (1970) 165–173.MathSciNetGoogle Scholar
  17. E.
    Algebraic K-theory, Evanston 1976, Lecture Notes in Math.551 (Springer 1976);Google Scholar
  18. FH.
    T. Fack andP. de la Harpe,Sommes de commutateurs dans les algèbres de von Neumann finies continues, Ann. Inst. Fourier 30 (1980) 49–73.Google Scholar
  19. F1.
    A. Fathi,Le groupe des transformations de [0, 1] qui préservent la mesure de Lebesgue est un groupe simple, Israel J. Math.29 (1978) 302–308.MathSciNetGoogle Scholar
  20. F2.
    A. Fathi,Structure of the group of homeomorphisms preserving a good measure on a compact manifold, Ann. scient. Ec. Norm. Sup. (4)13 (1980) 45–93.MathSciNetGoogle Scholar
  21. Hal.
    P. R. Halmos,A Hilbert space problem book, Van Nostrand 1967.Google Scholar
  22. H1.
    P. de la Harpe,Sous-groupes distingués du groupe unitaire et du groupe général linéaire d’un espace de Hilbert, Comment. Math. Helv.51 (1976) 241–257.MathSciNetGoogle Scholar
  23. H2.
    P. de la Harpe,Les extensions de gl(E)par un noyau de dimension finie sont triviales, J. Functional Analysis33 (1979) 362–373.CrossRefGoogle Scholar
  24. H3.
    P. de la Harpe,Classical groups and classical Lie algebras of operators, Proc. Symp. Pure Math. 381 (Amer. Math. Soc. 1982) 477–513.Google Scholar
  25. He.
    M. Herman, seeProblèmes in Journées sur la géométrie de la dimension infinie, Bull. Soc. Math. France, supp.46 (1976) 189–190.Google Scholar
  26. Hi.
    G. Higman,On infinite simple permutation groups, Publ. Math. Debrecen3 (1953–4) 221–226.MathSciNetGoogle Scholar
  27. Hu.
    D. Husemoller,Fibre bundles, McGraw Hill 1966.Google Scholar
  28. Ka.
    M. Karoubi,K-theory, an introduction, Springer 1978.Google Scholar
  29. Ke.
    M. Keane,Contractibility of the automorphism group of a nonatomic measure space, Proc. Amer. Math. Soc.26 (1970) 420–422.CrossRefMathSciNetGoogle Scholar
  30. Ker.
    M. Kervaire,Multiplicateurs de Schur et K-théorie. In “Essays on Topology and related Topics”, Mémoires dédiés à Georges de Rham, A. Haefliger and R. Narasimhan ed., Springer 1970.Google Scholar
  31. Ku.
    N. Kuiper,The homotopy type of tue unitary group of a Hilbert space, Topology3 (1965) 19–30.CrossRefMathSciNetGoogle Scholar
  32. LT.
    J. Lindenstrauss andL. Tzafriri,Classical Banach spaces I, sequence spaces, Springer 1970.Google Scholar
  33. Ma.
    G. W. Mackey,Mathematical foundations of quantum mechanics, Benjamin 1963.Google Scholar
  34. M.
    J. Mather,The vanishing of the homology of certain groups of homeomorphisms, Topology10 (1971) 297–298.CrossRefMathSciNetGoogle Scholar
  35. Mi.
    J. A. Mingo,On the contractibility of the unitary group of the Hilbert space over a C * -algebra. Thesis, Halifax 1981.Google Scholar
  36. P.
    S. B. Priddy,On Ω S and the infinite symmetric group, Proc. Symp. Pure Math.22 (Amer. Math. Soc. 1971) 217–220.Google Scholar
  37. Q1.
    D. Quillen,Higher algebraic K-theory: I. In “AlgebraicK-theory I, Battelle Institute conference 1972”, Lecture Notes in Math.341 (Springer 1973) 85–147.Google Scholar
  38. Q2.
    D. Quillen,Characteristic classes of representations. In “AlgebraicK-theory, Evanston 1976”, Lecture Notes in Math.551 (Springer 1976) 189–216.Google Scholar
  39. Re.
    P. L. Renz,The contractibility of the homeomorphism group of some product spaces, Math. Scand.28 (1971), 182–188.MathSciNetGoogle Scholar
  40. R.
    A. Rosenberg,The structure of the infinite general linear group, Ann. of Math.68 (1958) 278–294.CrossRefMathSciNetGoogle Scholar
  41. SW.
    C.-H. Sah andJ. B. Wagoner,Second homology of Lie groups made discrete, Comm. Alg.5 (1977) 611–642.MathSciNetGoogle Scholar
  42. SU.
    J. Schreier andS. Ulam,Über die Permutationsgruppe der natürlichen Zahlenfolge, Studia Math.4 (1933) 134–141.Google Scholar
  43. Se.
    G. Segal,Classifying spaces related to foliations, Topology17 (1978) 367–382.CrossRefMathSciNetGoogle Scholar
  44. Sp.
    E. H. Spanier,Algebraic topology, McGraw Hill 1966.Google Scholar
  45. St.
    J. Stern,Le groupe des isométries d’un espace de Banach, Studia Math.54 (1979) 139–149.Google Scholar
  46. W.
    J. B. Wagoner,Delooping classifying spaces in algebraic K-theory, Topology11 (1972) 349–370.CrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag 1983

Authors and Affiliations

  • Pierre de la Harpe
    • 1
    • 2
  • Dusa McDuff
    • 1
    • 2
  1. 1.Section de mathématiquesGenève 24
  2. 2.Department of MathematicsSUNYStony Brook

Personalised recommendations