I'm trying to figure out what the transfer map looks like in a specific case. Here's the set up

Let $G$ be a group and $H$ a subgroup of finite index, and let $h_{i}$ for $i=1,..,n$, be coset representatives.

Now following Weibel I know that if $A$ is a $G$ module, then $Tr_{0} :H_{0}(G,A) \rightarrow H_{0}(H,A)$ is the map that sends a 0-cycle $a$ to $\sum_{i} h_{i}.a$. Now theres two things:

the thing is I want to work out what $Tr_{1}: H_{1}(G,A) \rightarrow H_{1}(H,A)$ does specifically, and how does $G$ act on the 1-cycles, since I'm not sure how to define an action on 1-cycles. So I was wondering if I could get some help/hints or maybe some good references, so far I have looked at Weibels intro to homological algebra and a little of Rotmans Homological algebra.

Thank you

Thank you

Cohomology of Groups, that's the definitive. A nice way to see the transfer is induced from the covering map of classifying spaces. Namely, if $\sigma$ is a cell of $BG$ then $\sum\tilde{\sigma}$ is a cell of $BH$ (i.e. all the lifts of $\sigma$). Then $Tr$ maps cochain $f$ to the cochain $\sigma\mapsto \sum f(\tilde{\sigma})$. – Chris Gerig Feb 14 '13 at 19:50