Characteristic classes for spherical fibrations with fibre-preserving free group actions

Benjamin M. Mann, Edward Y. Miller

Research output: Contribution to journalArticle

Abstract

Let G(H) be the monoid of H equivariant self maps of S(nV), the unit sphere of n copies of a finite dimension orthogonal representation V of a finite group H, stabilized over n in an appropriate way. Let SG(H) be the submonid of G(H) consisting of all degree 1 maps. If H1 is a subgroup of H there is a natural forgetful map SG(H) → SG(H1) and if Z is the center of H there is a natural action map BZ × SG(H) → SG(H) induced by the natural action of Z on H. The main results of this paper are the calculations of the Hopf algebra structures of H*(SG(Z/pn), Z/p) and H*(BSG(Z/pn), Z/p) for all n and all primes p, the calculations in homology of forgetful maps induced by the natural inclusions Z/pn-1 → Z/pn and, for H = Z/2, the calculation of the action map H*(R P, Z/2) ⊗ H*(BSG(Z/2), Z/2) → H* (BSG(Z/2), Z/2).

Original languageEnglish (US)
Pages (from-to)327-377
Number of pages51
JournalPacific Journal of Mathematics
Volume108
Issue number2
DOIs
StatePublished - Oct 1983

ASJC Scopus subject areas

  • Mathematics(all)

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