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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.

3 votes
Accepted

$G$-action on the integral homology of a compact surface

I don't see how to answer this is general, but the following partial result might be of interest to you. Theorem: If $H^1(S;\mathbb{Z}) \cong \mathbb{Z}^2 \oplus \mathbb{Z}[G]^{2k}$ then $G$ does not …
Oscar Randal-Williams's user avatar
15 votes
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Group Extensions and Line Bundles on $BG$

If $L \to BG$ is the complex line bundle, take the unit sphere bundle $S^1 \to S(L) \to BG$ and take $\pi_1$.
Oscar Randal-Williams's user avatar