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Questions about the branch of algebra that deals with groups.
1
vote
1
answer
430
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a small question about group homology
If a group G has a subgroup H of finite index which is torsion free, then does it satisfy $H_\ast (G,Q) = H_ \ast (H,Q)$? (probably it is very well known...)
4
votes
2
answers
1k
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homotopy invariant and coinvariant
Let $V$ be a chain complex, which is either $Z$ or $Z/2$ graded. A circle action on $V$ is
by definition an action of the dga $H_\ast(S^1)$. This consists of a map $D : V → V$ , which is of square zer …
6
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3
answers
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Do the homological dimension and cohomological dimension for a group agree?
Or equivalently, if $G$ is a group, do the projective and injective dimension of $Z$ (viewed as a $ZG$-module) agree?
Thanks!