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Questions about the branch of algebra that deals with groups.

1 vote
1 answer
430 views

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...)
Hao's user avatar
  • 113
4 votes
2 answers
1k views

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 …
Hao's user avatar
  • 113
6 votes
3 answers
2k views

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!
Hao's user avatar
  • 113