The Morava K-theory of homotopy orbit spaces: Some good results for Abelian permutation groups.

摘要

We show that EG xG X N is good whenever X is good and G < SigmaN is a finite Abelian permutation p-group. We begin with cyclic permutation groups G ≅ Z /pn < Sigmap n and examine K(s)*( EG xG Xpn ) via the Atiyah-Hirzebruch-Serre spectral sequence E*,*r&parl0;G,Xpn &parr0;&rArrr;K s*&parl0;EGxG Xpn&parr0; and the morphisms of spectral sequences E*,*rW,Xpn &rarrr;E*,*r G,Xpn induced from embeddings of G into various wreath products W. Using a strong form of induction we compute a K(s)*-basis for K(s)* EGxGXpn and show that EGxGXpn is good. We use these results about EGxGXpn for cyclic p-groups G < Sigma pn to establish that EG x G XN is good whenever X is good and G < SigmaN is a finite abelian permutation p-group.