Commentarii Mathematici Helvetici

, Volume 55, Issue 1, pp 302–313 | Cite as

Crossedn-fold extensions of groups and cohomology

  • Johannes Huebschmann
Article
Received:
  • 78 Downloads

Keywords

Abelian Group Normal Subgroup Cohomology Group Homotopy Type Group Homomorphism 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Blakers A. L.,Some relations between homology and homotopy groups, Ann. of Math.49 (1948), 428–461.CrossRefMathSciNetGoogle Scholar
  2. [2]
    Brown R. andHiggins Ph. J.,Sur les complexes croises, ω-groupoides, et T-complexes, C.R. Acad. Sci. Paris Série A285 (1977), 997–999.MATHMathSciNetGoogle Scholar
  3. [3]
    —,Sur les complexes croisés d'homotopie associés à quelques espaces filtrés, C.R. Acad. Sci. Paris Série A286 (1978), 91–93.MATHGoogle Scholar
  4. [4]
    —,On the connection between the second relative homotopy groups of some related spaces, Proc. London Math. Soc. (3)36 (1978), 193–212.MathSciNetGoogle Scholar
  5. [5]
    Brown R.,On the algebra of cubes, Preprint 1979.Google Scholar
  6. [6]
    Brown R.,Colimit theorems for relative homotopy groups. Preprint 1979.Google Scholar
  7. [7]
    Eilenberg S. andMacLane S.,Conomology theory in abstract groups. II. Group extensions with a non-Abelian kernel. Ann. of Math.48 (1947), 326–341.CrossRefMathSciNetGoogle Scholar
  8. [8]
    Hilton P. J.,An introduction to homotopy theory, Cambridge 1953.Google Scholar
  9. [9]
    Howie J.,Pullback functors and crossed complexes, preprint 1978.Google Scholar
  10. [10]
    Huebschmann J.,Verschränkte n-fache Erweiterungen von Gruppen und Cohomologie, Diss. ETH Nr. 5999, Eidg. Techn. Hochschule, Zürich 1977.Google Scholar
  11. [11]
    —Sur les premières différentielles de la suite spectrale cohomologique d'une extension de groupes, C.R. Acad. Sci. Paris Série A285 (1977), 929–931.MATHMathSciNetGoogle Scholar
  12. [12]
    —,Extensions de groupes et paires croisées, C.R. Acad. Sci. Paris Série A285 (1977), 993–995.MATHMathSciNetGoogle Scholar
  13. [13]
    Huebschmann J.,The first k-invariant, Quillen's space BG + and the construction of Kan and Thurston, Comm. Math. Helv.55 (1980).Google Scholar
  14. [14]
    Huebschmann J.,Automorphisms of group extensions and differentials in the Lyndon-Hochschild-Serre spectral sequence, submitted to J. of Algebra.Google Scholar
  15. [15]
    Huebschmann J.,Group extensions, crossed pairs, and an eight term exact sequence, in preparation.Google Scholar
  16. [16]
    MacLane S.,Cohomology theory in abstract groups. III. Operator homomorphisms of kernels. Ann. of Math.50 (1949), 736–761.CrossRefMathSciNetGoogle Scholar
  17. [17]
    —,Historical Note, J. of Algebra60 (1979), 319–320. Appendix to [27] below.CrossRefMathSciNetGoogle Scholar
  18. [18]
    — andWhitehead J. H. C.,On the 3-type of a complex, Proc. N.A.S.36 (1950), 41–48.MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    Peiffer R.,Über Identitäten zwischen Relationen, Math. Ann.121 (1949), 67–99.MATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    Reidemeister K.,Über Identitäten von Relationen, Abh. Math. Sem. Univ. Hamburg16 (1949), 114–118.MathSciNetMATHGoogle Scholar
  21. [21]
    Rinehart G. S.,Satellites and cohomology, J. of Alg.12 (1969), 295–329.MATHCrossRefMathSciNetGoogle Scholar
  22. [22]
    Whitehead J. H. C.,On adding relations to homotopy groups, Ann. of Math.42 (1941), 409–428.CrossRefMathSciNetGoogle Scholar
  23. [23]
    —,On incidence matrices, nuclei and homotopy types, Ann. of Math.42 (1941), 1197–1139.CrossRefMathSciNetGoogle Scholar
  24. [24]
    —,Note on a previous paper entitled “On adding relations to homotopy groups”, Ann. of Math.47 (1946), 806–810.CrossRefMathSciNetGoogle Scholar
  25. [25]
    —,Combinatorial homotopy. II. Bull. Amer. Math. Soc.55 (1949), 453–496.MATHMathSciNetCrossRefGoogle Scholar
  26. [26]
    —,Simple homotopy types, Amer. J. Math.72 (1950), 1–57.MATHCrossRefMathSciNetGoogle Scholar
  27. [27]
    Holt O. F.,An Interpretation of the Cohomology Groups H n (G, M), J. of Alg.60 (1979), 307–318.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag 1980

Authors and Affiliations

  • Johannes Huebschmann
    • 1
  1. 1.Mathematisches Institut der UniversitätHeidelbergW-Germany

Personalised recommendations