Skip to main content

On the localization theorem at the cochain level and free torus actions

Part of the Lecture Notes in Mathematics book series (2766,volume 1172)

Keywords

  • Minimal Model
  • Algebraic Closure
  • Equivariant Cohomology
  • Cohomology Theory
  • Exterior Algebra

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, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. ALLDAY, C.: On the rank of a space, Trans.Amer.Math.Soc. 166, 173–185 (1972)

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. ALLDAY, C.: On the rational homotopy of fixed point sets of torus actions. Topology 17, 95–100 (1978)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. ALLDAY, C. and HALPERIN, S.: Lie group actions on spaces of finite rank. Quart.J.Math. Oxford (2) 29, 69–76 (1978)

    MathSciNet  MATH  Google Scholar 

  4. ALLDAY, C.J. and HALPERIN, S.: Sullivan-de Rham theory for rational Alexander-Spanier cohomology, Houston J.Math., to appear.

    Google Scholar 

  5. ATIYAH, M.F.-BOTT, R.: The moment map and equivariant cohomology. Topology 23, 1–28 (1984)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. BOREL, A.: Seminar on Transformation groups. Annals of Math.Studies, No. 46, Princeton, New Jersey: Princeton Univ. Press 1960

    MATH  Google Scholar 

  7. BREDON, G.E.: Introduction to Compact Transformation Groups. New-York-London: Academic Press 1972

    MATH  Google Scholar 

  8. BROWDER, W.: Cohomology and group actions. Invent Math. 71, 599–607 (1983)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. BROWN, E.H.: Twisted tensor products, I. Ann. of Math. 69, 223–246 (1959)

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. CARLSSON, G.: On the non-existence of free actions of elementary abelian groups on products of spheres. Amer.J.Math. 102, 1147–1157 (1980)

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. CARLSSON, G.: On the rank of abelian groups acting freely on (Sn)k. Invent.Math. 69, 393–400 (1982)

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. CARLSSON, G.: On the homology of finite free (ℤ/2)n-complexes, Invent.Math. 74, 139–147 (1983)

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. CHANG, T. and SKJELBRED, T.: The topological Schur lemma and related results, Ann. of Math., 100 (1974), 307–321.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. DOLD, A.: Zur Homotopietheorie der Kettenkomplexe. Math.Ann. 140, 278–298 (1960)

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. GRIVEL, P.P.: Thèse, Universitè de Genève, 1977

    Google Scholar 

  16. HALPERIN, S.: Lectures on minimal models, Publications interne de l'U.E.R. de Mathématiques, Université de Lille 1977

    Google Scholar 

  17. HALPERIN, S.: Rational homotopy and torus actions. (preprint)

    Google Scholar 

  18. HSIANG, W.Y.: Cohomology Theory of Topological Transformation Groups. Berlin-Heidelberg-New York: Springer 1975

    CrossRef  MATH  Google Scholar 

  19. ILLMAN, S.: Equivariant singular homology and cohomology for actions of compact Lie groups. Springer, Lecture Notes in Math. Vol. 298, 403–415 (1972)

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. MATUMOTO, T.: On G-CW complexes and a theorem of J.H.C. Whitehead. J.Fac.Sci.Univ. Tokyo Sect. IA/Math. 18, 363–374 (1971)

    MathSciNet  MATH  Google Scholar 

  21. PUPPE, V.: Cohomology of fixed point sets and deformation of algebras. manuscripta math. 23, 343–354 (1978)

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. PUPPE, V.: P.A. Smith theory via deformations, in "Homotopie algébrique et algébre locale", Astérisque 113–114, SociétéMathématique de France, 1984

    Google Scholar 

  23. QUILLEN, D.: The spectrum of an equivariant cohomology ring: I. Ann. of Math. 94 (1971). 549–572

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. QUILLEN, D.: The spectrum of an equivariant cohomology ring: II. Ann. of Math. 94 (1971). 573–602

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. SEYMOUR, R.M.: On G-cohomology theories and Künneth formulae, Current Trends in Algebraic Topology, CMS Conference Proceedings, Vol. 2, part 1, Amer.Math.Soc., Providence, 1982.

    Google Scholar 

  26. SULLIVAN, D.: Infinitesimal computations in topology. Inst. Hautes Êtudes Sci. Publ. Math. No. 47, 269–331 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Allday, C., Puppe, V. (1985). On the localization theorem at the cochain level and free torus actions. In: Smith, L. (eds) Algebraic Topology Göttingen 1984. Lecture Notes in Mathematics, vol 1172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074421

Download citation

  • DOI: https://doi.org/10.1007/BFb0074421

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16061-8

  • Online ISBN: 978-3-540-39745-8

  • eBook Packages: Springer Book Archive