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Homotopy theory, homological algebra, algebraic treatments of manifolds.
5
votes
Extensions of topological groups
Bugs is right. If $G$ is locally compact abelian and multiplication by $2$ (or squaring) is an automorphism of $G$, then $H^2(G,U(1))$ is isomorphic to the group of alternating bi-characters $G\times …
3
votes
The extension class of a finite Heisenberg group
I believe that your conjecture is equivalent to Theorem 3.5 in the paper Locally Compact Abelian Groups with Symplectic Self-duality, Advances in Mathematics, volume 225, pages 2429-2454, 2010.