The rational characteristic class ring for oriented S^n x S^n-fibrations injects into smooth bundle cohomology, producing non-trivial classes in all degrees detected by bundles from cyclic subgroups of a finite-index subgroup of SL_2(Z).
S.Cohomology of Groups; Graduate Texts in Mathematics, Vol
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Representations of generalized digroups are equivalent to modules over an enveloping algebra, with Maschke-type splitting on the ρ-side controlled by cohomology and a spectral sequence under a group-component condition.
Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.
Introduces the group E^ws_TA(A,B) of weakly split extensions in topological Abelian groups, gives descriptions as continuous sum structures on B×A and as a cocycle quotient Z_c/B_c, relates it to ordinary extensions via a six-term exact sequence, and supplies examples for discrete groups with Bohr t
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Rational characteristic classes of bundles with fibre a product of spheres
The rational characteristic class ring for oriented S^n x S^n-fibrations injects into smooth bundle cohomology, producing non-trivial classes in all degrees detected by bundles from cyclic subgroups of a finite-index subgroup of SL_2(Z).
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Cohomological Maschke's Theorem for Generalized Digroups
Representations of generalized digroups are equivalent to modules over an enveloping algebra, with Maschke-type splitting on the ρ-side controlled by cohomology and a spectral sequence under a group-component condition.
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On formality of diagrams of Eilenberg-MacLane spaces
Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.
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Weak split extensions of topological Abelian groups
Introduces the group E^ws_TA(A,B) of weakly split extensions in topological Abelian groups, gives descriptions as continuous sum structures on B×A and as a cocycle quotient Z_c/B_c, relates it to ordinary extensions via a six-term exact sequence, and supplies examples for discrete groups with Bohr t
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