HOMOTOPY FIXED POINT SET OF THE HOMOTOPY FIBRE

  • Published : 1999.11.01

Abstract

Let X be a p-compace groyp, Y -> X bd a p-compact-subgroup of X and G -> X be a p-compact toral subgroup of X with $(X/Y)^{hG} \neq 0$. In this paper we show that the homotopy fixed point set of the homotopy fibre $(X/Y)^{hG}$ is $F_p$-finite.

Keywords

References

  1. Lecture Notes in Math. Homotopy limits, completions and localizations A. K. Bousfield;D. K. Kan
  2. Transformation Groups T. tom Dieck
  3. Ann. of Math. v.139 Homotopy fixed point methods for Lie groups and finite loop spaces W. G. Dwyer;C. W. Wilkerson
  4. Contemp. Math., Amer. Math. Soc. v.181 The center of a-compact groups W. G. Dwyer;C. W. Wilkerson
  5. Annals of Math. v.120;121 The Sullivan conjecture on maps from classifying spaces H. R. Miller
  6. J. reine. angew. Math. v.456 Centers and finite converings of finite loop spaces J. M. MΦller;D. Notbohm
  7. Quarterly J. of Math. Unstable splittings of classifying spaces of p-compact groups D. Notbohm
  8. Handbook of algebraic topology Classifying spaces and finite loop spaces D. Notbohm
  9. J. Pure. Appl. Algebra v.4 Subgroups of finite dimensional topological groups D. L. Rector
  10. Algebraic Topology E. Spainer