Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $G_1$ and $G_2$ be groups and let $M$ be a vector space equipped with actions of $G_1$ and $G_2$. The free product $G_1 \ast G_2$ thus acts on $M$. How can one compute the twisted group homology $H_{\ast}(G_1 \ast G_2;M)$ in terms of $H_{\ast}(G_1;M)$ and $H_{\ast}(G_2;M)$? Since I doubt that $H_{\ast}(G_1;M)$ and $H_{\ast}(G_2;M)$ are enough to completely determine $H_{\ast}(G_1 \ast G_2;M)$, I guess my question more precisely is what additional information is needed?

share|improve this question
3  
@Lewis: You have Meyer-Vietoris sequence, see Ken Brown's book "Cohomology of groups". Situation is the same as with topological spaces since $H_*(G,M)=H_*(K(G,1), {\mathbb M})$, where ${\mathbb M}$ is an appropriate sheaf on $K(G,1)$. –  Misha Mar 27 '12 at 23:39

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.