The homology of Cn+1-Spaces, n≥0

  • Fred Cohen
Part of the Lecture Notes in Mathematics book series (LNM, volume 533)


Spectral Sequence Braid Group Loop Space Fundamental Class Serre Spectral Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Araki and T. Kudo, Topology of Hn-spaces and H-squaring operations. Mem. Fac. Sci. Kyūsyū Univ. Ser. A, 1956, 85–120.Google Scholar
  2. 2.
    V. I. Arnold, The cohomology ring of the colored braid group. Math. Zametki, 2(1969), 227–231.Google Scholar
  3. 3.
    V. I. Arnold, On a class of algebraic functions and cohomologies of fiber tails. Uspeki Mat. Nauk S.S.S.R., 23(1968), 247–248.Google Scholar
  4. 4.
    E. Artin, Theory of braids. Annals of Math., 48(1947), 101–126.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    R. Bott and H. Samelson, On the Pontrjagin product in spaces of paths, Comment. Math. Helv., 27(1953), 320–337.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    W. Browder, Homology operations and loop spaces, Ill. J. Math., 4(1960), 347–357.MathSciNetzbMATHGoogle Scholar
  7. 7.
    H. Cartan and S. Eilenberg, Homological Algebra. Princeton: Princeton University Press, 1956.zbMATHGoogle Scholar
  8. 8.
    E. Dyer and R. K. Lashof, Homology of iterated loop spaces. Amer. J. Math., 1962, 35–88.Google Scholar
  9. 9.
    E. Fadell and L. Neuwirth, Configuration spaces. Math. Scand., 10(1962), 119–126.MathSciNetzbMATHGoogle Scholar
  10. 10.
    R. Fox and L. Neuwirth, The braid groups. Math. Scand., 10(1962), 119–126.MathSciNetzbMATHGoogle Scholar
  11. 11.
    M. Hall, A basis for free Lie rings and higher commutators in free groups. Proc. Am. Soc., 1(1950), 575–581.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    P. Hilton, On the homotopy groups of a union of spheres. Comment. Math. Helv., 29(1955), 59–92.MathSciNetCrossRefGoogle Scholar
  13. 13.
    P. Hilton, Homotopy Theory and Duality. Gordon and Breach, 1965.Google Scholar
  14. 14.
    N. Jacobson, Lie Algebras. Interscience Tracts in Pure and Applied Math., no. 10, Interscience, New York, 1962.zbMATHGoogle Scholar
  15. 15.
    S. MacLane, Homology. Academic Press, 1963Google Scholar
  16. 16.
    (A) J. P. May, A general algebraic approach to Steenrod operations. The Steenrod Algebra and its Applications, Lecture Notes in Math., Vol. 168, Springer Verlag, 1970, 153–231.Google Scholar
  17. 17.
    (G) J. P. May, The Geometry of Iterated Loop Spaces, Lecture Notes in Math., vol. 271, Springer Verlag, 1972.Google Scholar
  18. 18.
    (G′) J. P. May, E ring spaces and permutative categories.Google Scholar
  19. 19.
    (I) J. P. May, The homology of E spaces.Google Scholar
  20. 20.
    R. J. Milgram, Iterated loop spaces, Ann. of Math., 84(1966), 386–403.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    H. Samelson, A connection between the Whitehead and the Pontrjagin product. Am. J. Math. 75(1953), 744–752.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    G. Segal, Configuration spaces and iterated loop spaces. Invent. Math., 21(1973), 213–221.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    R. G. Swan, The p-period of a finite group. Ill. J. Math. 4 (1960), 341–346.MathSciNetzbMATHGoogle Scholar
  24. 24.
    W. Browder, Torsion in H-spaces. Ann. of Math. 74(1961), 24–51.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    V. Snaith, A stable decomposition for ΩnΣnX. J. London Math. Soc., 8(1974).Google Scholar
  26. 26.
    F. Cohen, Cohomology of braid spaces. B.A.M.S. 79(1973), 761–764.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    F. Cohen, Homology of Ωn+1Σn+1X and Cn+1X, n>0. B.A.M.S., 79(1973), 1236–1241.CrossRefGoogle Scholar
  28. 28.
    F. Cohen, Splitting certain suspensions via self-maps. To appear in Ill. J. Math..Google Scholar
  29. 29.
    D. B. Fuks, Cohomologies of the braid groups mod 2. Functional Analysis and its Applications, 4 (1970), 143–151.CrossRefzbMATHGoogle Scholar
  30. 30.
    F. Cohen and L. Taylor, The cohomology of configuration spaces and of braid spaces on manifolds. (In preparation)Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Fred Cohen

There are no affiliations available

Personalised recommendations