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Homotopy approximations for classifying spaces of compact lie groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 1370)

Keywords

  • Spectral Sequence
  • Full Subcategory
  • Isotropy Subgroup
  • Contravariant Functor
  • Orthogonal Representation

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References

  1. Bousfield, A.K. and Kan, D.M., Homotopy limits, completions and localizations, Lecture Notes in Math. Vol. 304, Springer 1972.

    Google Scholar 

  2. Bredon, G., Introduction to compact transformation groups, Academic Press, 1972.

    Google Scholar 

  3. Conner, P.E. and Montgomery, D., An example for SO(3), Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 1918–1922.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. tom Dieck, T., Transformation Groups and Representation Theory, Lecture Notes in Math. Vol 766, Springer 1979.

    Google Scholar 

  5. Dwyer, W., Miller, H., and Wilkerson, C., The homotopic uniqueness of BS 3 , Preprint.

    Google Scholar 

  6. Friedlander, E. and Mislin, G., Locally finite approximations of Lie groups I., Inventiones Math. 83 (1986), 425–436.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Lewis, L.G., May, J.P., and McClure, J.E., Ordinary RO(G)-graded cohomology, Bull. Amer. Math. Soc. 4 (1981), 208–212.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Lewis, L.G., May, J.P., and Steinberger, M., Equivariant Stable Homotopy Theory, Lecture Notes in Math. Vol. 1213, Springer, 1986.

    Google Scholar 

  9. May, J.P., Classifying spaces and fibrations, Memoirs Amer. Math. Soc. 155 (1986).

    Google Scholar 

  10. Mislin, G., The homotopy classification of self-maps of infinite quaterionic projective space, Quarterly J. of Math. Oxford 38 (1987), 245–257.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Oliver, R., Fixed-point sets of group actions on finite acyclic complexes, Comment. Math. Helv. 50 (1975), 155–177.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Oliver, R., A proof of the Conner conjecture, Annals of Math. 103 (1976), 637–644.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Tornehave, J., Equivariant maps of spheres with conjugate orthogonal actions, Canadian Math. Soc. Conference Proceedings Vol. 2, Part 2, 1982, 275–301.

    MathSciNet  MATH  Google Scholar 

  14. Willson, S.J., Equivariant homology theories on G-complexes, Trans. Amer. Math. Soc. 212 (1975), 155–171.

    MathSciNet  MATH  Google Scholar 

  15. Miller, H., The Sullivan conjecture, Bull. Amer. Math. Soc. 9 (1983), 75–79.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Dwyer, W., and Kan, D.M., A classification theorem for diagrams of simplicial sets, Topology 23 (1984), 139–155.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1989 Springer-Verlag

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Jackowski, S., McClure, J.E. (1989). Homotopy approximations for classifying spaces of compact lie groups. In: Carlsson, G., Cohen, R., Miller, H., Ravenel, D. (eds) Algebraic Topology. Lecture Notes in Mathematics, vol 1370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085230

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  • DOI: https://doi.org/10.1007/BFb0085230

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51118-2

  • Online ISBN: 978-3-540-46160-9

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