Skip to main content

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

  • Conference paper
  • First Online:
Book cover Algebra, Algebraic Topology and their Interactions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1183))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. André, Hopf algebras with divided powers, J. Algebra 18 (1971), 19–50.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. André, Homologie des Algèbres Commutatives, Springer, Berlin 1974.

    Book  MATH  Google Scholar 

  3. M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, 1969.

    Google Scholar 

  4. L.L. Avramov, Local algebra and rational homotopy, in Homotopie Algébrique et Algèbre Locale, Astérisque 113/114 (1984), 15–43.

    Google Scholar 

  5. L.L. Avramov, Homotopy Lie algebras for commutative rings and DG algebras, to appear.

    Google Scholar 

  6. 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. L. Carroll, Through the Looking Glass and What Alice Found There, Macmillan 1871.

    Google Scholar 

  8. Y. Felix and J.-C. Thomas, Sur l'opération de l'holonomie rationnelle, these proceedings.

    Google Scholar 

  9. 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.

    MATH  Google Scholar 

  10. 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. S. Halperin, Lectures on Minimal Models, Mém. de la Soc. Math. de France 9/10, 1983.

    Google Scholar 

  12. S. Halperin and J.-M. Lemaire, Suites inertes dans les algèbres de Lie graduées, preprint. (To appear in Math. Scand.)

    Google Scholar 

  13. G. Levin and L.L. Avramov, Factoring out the socle of a local Gorenstein ring, J. Algebra 55 (1978), 74–83.

    Article  MathSciNet  MATH  Google Scholar 

  14. 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. H. Matsumura, Commutative Algebra 2nd ed., Benjamin/Cummings, Reading, Mass. 1980.

    MATH  Google Scholar 

  16. J.W. Milnor and J.C. Moore, On the structure of Hopf algebras, Annals Math. 81 (1965), 211–264.

    Article  MathSciNet  MATH  Google Scholar 

  17. D. Quillen, Homotopical Algebra, Lecture Notes in Math. 43 (1967), Springer Verlag.

    Google Scholar 

  18. D. Quillen, On the (co)-homology of commutative rings, Proc. Symp. Pure Math. (17), Amer. Math. Soc. 1970, 65–87.

    Google Scholar 

  19. 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. G. Sjödin, Hopf algebras and derivations, J. Algebra 64 (1980), 218–229.

    Article  MathSciNet  MATH  Google Scholar 

  21. D. Sullivan, Infinitesimal computations in topology, Publ. Math. IHES 47 (1978), 269–331.

    Article  MATH  Google Scholar 

  22. J. Tate, Homology of noetherian rings and local rings, Illinois J. Math. 1 (1957), 14–27.

    MathSciNet  MATH  Google Scholar 

  23. G. Whitehead, Elements of Homotopy Theory, Springer Verlag, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jan-Erik Roos

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Avramov, L., Halperin, S. (1986). Through the looking glass: A dictionary between rational homotopy theory and local algebra. In: Roos, JE. (eds) Algebra, Algebraic Topology and their Interactions. Lecture Notes in Mathematics, vol 1183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075446

Download citation

  • DOI: https://doi.org/10.1007/BFb0075446

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16453-1

  • Online ISBN: 978-3-540-39790-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics