Title of Paper: An elementary invariant problem and general linear group
cohomology restricted to the diagonal subgroup
Author: Marian F. Anton
AMS Classification numbers: 57T10, 20J05, 19D06, 55R40
Address of Author: University of Sheffield, Department of Pure Mathematics,
Hicks Building, Sheffield, S3 7RH, U.K.
Email address of Author: Marian.Anton@imar.ro
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.