An elementary invariant problem and general linear group cohomology restricted to the diagonal subgroup
Author:
Marian F. Anton
Journal:
Trans. Amer. Math. Soc. 355 (2003), 23272340
MSC (2000):
Primary 57T10, 20J05; Secondary 19D06, 55R40
Published electronically:
January 27, 2003
MathSciNet review:
1973992
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Abstract: Conjecturally, for an odd prime and a certain ring of integers, the stable general linear group and the étale model for its classifying space have isomorphic mod 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 is regular and certain homology classes for vanish. We check that this criterion is satisfied for as evidence for the conjecture.
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Additional Information
Marian F. Anton
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom and IMAR, P.O. Box 1764, Bucharest, Romania 70700
Address at time of publication:
Department of Mathematics, University of Kentucky, 715 POT, Lexington, Kentucky 405060027
Email:
Marian.Anton@imar.ro
DOI:
http://dx.doi.org/10.1090/S0002994703032550
PII:
S 00029947(03)032550
Keywords:
Etale model,
linear group,
cohomology,
invariants
Received by editor(s):
May 1, 2002
Received by editor(s) in revised form:
November 14, 2002
Published electronically:
January 27, 2003
Article copyright:
© Copyright 2003
American Mathematical Society
