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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Proposes a refinement of the Swampland Cobordism Conjecture for duality groups, arguing that diverging commutator widths necessitate infinitely many duality defects to realize monodromies in 9d supergravity bordisms.
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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