An elementary invariant problem and general linear group cohomology restricted to the diagonal subgroup, by Marian F. Anton

Conjecturally, for p an odd prime and R a certain ring of p-integers, the stable general linear group GL(R) and the etale model for its classifying space have isomorphic mod p cohomology rings. In particular, these two cohomology rings should have the same image with respect to the restriction map to the diagonal subgroup. We show that a strong unstable version of this last property holds for any rank if p is regular and certain homology classes for SL(2,R) vanish.


Marian F. Anton <Marian.Anton@imar.ro>