Skip to main content
SpringerLink
Log in

LS category of classifying spaces and 2-cones

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

LetX be a simply connected space of LS category two. We show that the LS category ofB aut X is not finite whenX is not coformal or satisfies Poincaré duality.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H.J. Baues and J.M. Lemaire,Minimal models in homotopy theory, Math. Ann. 225 (1977), 219–242.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Dold,Halbexacte Homotopiefunktoren, Lecture notes in mathematics, vol. 12 (1966), Springer-Verlag.

  3. A. Dold and R. Lashoff,Principal quasi-fibrations and fibre homotopy equivalence of bundles, Illinois J. Math. 3 (1959), 285–305.

    MATH  MathSciNet  Google Scholar 

  4. E. Dror and A. Zabrodsky,Unipotency and nilpotency in homotopy equivalences, Topology 18 (1979), 187–197.

    Article  MATH  MathSciNet  Google Scholar 

  5. Y. Félix and S. Halperin,Rational LS-category and its applications, Trans. A.M.S. 273 (1982), 1–17.

    Article  MATH  Google Scholar 

  6. Y. Félix, S. Halperin, C. Jacobsson, C. Löfwall and J.-C. Thomas,The radical of the homotopy Lie algebra, Amer. J. of Math. 110 (1988), 301–322.

    Article  MATH  Google Scholar 

  7. Y. Félix, S. Halperin and J.-C. Thomas,Engel elements in the homotopy Lie algebra, J. of Algebra 144 (1991), 67–78.

    Article  MATH  Google Scholar 

  8. Y. Félix, S. Halperin, J.-M. Lemaire et J.C. Thomas.Mod p loop space homology, Inventiones math. 95 (1989), 247–262.

    Article  MATH  Google Scholar 

  9. Y. Félix and J.-C. Thomas,Sur la structure des espaces de LS catégorie deux, Ill. Jour. Math. 30 (1986), 574–593.

    MATH  Google Scholar 

  10. J.-B. Gatsinzi,LS category of classifying spaces, II, Bul. Belg. Math. Soc. 3 (1996), 243–248.

    MATH  MathSciNet  Google Scholar 

  11. J.-B. Gatsinzi,The homotopy Lie algebra of classifying spaces, to appear in J. Pure and Applied Algebra.

  12. D.H. Gottlieb,Evaluation subgroups of homotopy groups, Amer. J. of math. 91 (1969), 729–756.

    Article  MATH  MathSciNet  Google Scholar 

  13. S. Halperin,Lectures on minimal models, Mémoire de la Société Mathématique de France, 9–10, 1983.

  14. S. Halperin and J.M. Lemaire,Suites inertes dans les algèbres de Lie Graduées, Math. Scand. 61 (1987), 39–67.

    MATH  MathSciNet  Google Scholar 

  15. P. Lambrechts,Croissance des nombres de Betti rationnels de l’espace des lacets libres d’un espace biformel, Rapport 209, Séminaire de Mathématique, Université Catholique de Louvain, 1992.

  16. D. Quillen,Rational homotopy theory, Annals of Math. (2) 90 (1969), 205–295.

    Article  MathSciNet  Google Scholar 

  17. M. Schlessinger and J. Stasheff,Deformations theory and rational homotopy type, preprint.

  18. J. Stasheff,Rational Poincaré duality spaces, Illinois J. of Math. 27 (1983), 104–109.

    MATH  MathSciNet  Google Scholar 

  19. D. Sullivan,Infinitesimal computations in topology, Publ. Math. I.H.E.S. 47 (1977), 269–331.

    MATH  MathSciNet  Google Scholar 

  20. D. Tanré,Homotopie rationnelle; modèles de Chen, Quillen, Sullivan, Lecture notes in mathematics, vol. 1025, Springer-Verlag, 1983.

  21. G.H. Toomer,Lusternik-Schnirelmann category and Moore spectral sequence, Math. Z. 138 (1974), 123–143.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Freie Universität Berlin, Germany

    J. -B. Gatsinzi

Authors
  1. J. -B. Gatsinzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. -B. Gatsinzi.

Additional information

Supported by a Humboldt-Stiftung research fellowship.

This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gatsinzi, J.B. LS category of classifying spaces and 2-cones. Manuscripta Math 94, 243–252 (1997). https://doi.org/10.1007/BF02677850

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02677850

Subject Classifications

Key words

Search

Navigation