Advertisement

Through the looking glass: A dictionary between rational homotopy theory and local algebra

  • Luchezar Avramov
  • Stephen Halperin
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1183)

Keywords

Hopf Algebra Spectral Sequence Local Ring Homotopy Type Homotopy Theory 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A1]
    M. André, Hopf algebras with divided powers, J. Algebra 18 (1971), 19–50.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [A2]
    M. André, Homologie des Algèbres Commutatives, Springer, Berlin 1974.CrossRefzbMATHGoogle Scholar
  3. [A-M]
    M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, 1969.Google Scholar
  4. [Av1]
    L.L. Avramov, Local algebra and rational homotopy, in Homotopie Algébrique et Algèbre Locale, Astérisque 113/114 (1984), 15–43.Google Scholar
  5. [Av2]
    L.L. Avramov, Homotopy Lie algebras for commutative rings and DG algebras, to appear.Google Scholar
  6. [B-G]
    A.K. Bousfield and V.K.A.M. Gugenheim, On the PL De Rham Theory and rational homotopy type, Memoirs Amer. Math. Soc. 179 (1976).Google Scholar
  7. [C]
    L. Carroll, Through the Looking Glass and What Alice Found There, Macmillan 1871.Google Scholar
  8. [F-T]
    Y. Felix and J.-C. Thomas, Sur l'opération de l'holonomie rationnelle, these proceedings.Google Scholar
  9. [G-L]
    T.H. Gulliksen and G. Levin, Homology of Local Rings, Queen's papers in Pure and Applied Mathematics — No. 20 Queen's University, Kingston, Ontario, 1969.zbMATHGoogle Scholar
  10. [G-M]
    V.K.A.M. Gugenheim and J.P. May, On the Theory and Application of Differential Torsion products, Memoirs of the Amer. Math. Soc. 142 (1974).Google Scholar
  11. [Ha]
    S. Halperin, Lectures on Minimal Models, Mém. de la Soc. Math. de France 9/10, 1983.Google Scholar
  12. [Ha-Le]
    S. Halperin and J.-M. Lemaire, Suites inertes dans les algèbres de Lie graduées, preprint. (To appear in Math. Scand.)Google Scholar
  13. [L-Av]
    G. Levin and L.L. Avramov, Factoring out the socle of a local Gorenstein ring, J. Algebra 55 (1978), 74–83.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [M]
    J.C. Moore, Algèbre homologique et homologie des espaces classifiants, Séminaire H. Cartan, École Normale Supérieure, 1959–1960, Exposé 7, Secrétariat Math., Paris, 1961.Google Scholar
  15. [Ma]
    H. Matsumura, Commutative Algebra 2nd ed., Benjamin/Cummings, Reading, Mass. 1980.zbMATHGoogle Scholar
  16. [M-M]
    J.W. Milnor and J.C. Moore, On the structure of Hopf algebras, Annals Math. 81 (1965), 211–264.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [Q1]
    D. Quillen, Homotopical Algebra, Lecture Notes in Math. 43 (1967), Springer Verlag.Google Scholar
  18. [Q2]
    D. Quillen, On the (co)-homology of commutative rings, Proc. Symp. Pure Math. (17), Amer. Math. Soc. 1970, 65–87.Google Scholar
  19. [R]
    J.-E. Roos, Relations between the Poincaré-Betti series of loop spaces and of local rings, Lecture Notes in Math. 740, 285–322, Springer Verlag, Berlin 1979.Google Scholar
  20. [Sj]
    G. Sjödin, Hopf algebras and derivations, J. Algebra 64 (1980), 218–229.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [Su]
    D. Sullivan, Infinitesimal computations in topology, Publ. Math. IHES 47 (1978), 269–331.CrossRefzbMATHGoogle Scholar
  22. [T]
    J. Tate, Homology of noetherian rings and local rings, Illinois J. Math. 1 (1957), 14–27.MathSciNetzbMATHGoogle Scholar
  23. [W]
    G. Whitehead, Elements of Homotopy Theory, Springer Verlag, 1981.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Luchezar Avramov
    • 1
  • Stephen Halperin
    • 2
  1. 1.Institute of MathematicsUniversity of SofiaSofiaBulgaria
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

Personalised recommendations