# corestriction and transversals

Is the corestriction map from a subgroup H to a group G, on the first Tate cohomology group H^1, dependent on the chosen transversal of H is G?

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No, because the map on cochains is $f\mapsto \sum_{g\in G/H}gfg^{-1}$ where $f$ is $H$-linear, so that any other coset representative $gh$ would not have any effect.
This shows that $cor^G_H$ is independent of the choice of transversal on the level of cohomology. But in that paper of Eunmi Choi, a $\textit{different}$ map on the level of cochains is given (using the bar resolution), which also induces $cor^G_H$ on cohomology, and this $\textit{is}$ dependent on the choice of transversal, as is shown in that paper. But all such images lie in the same cohomology class.
Nevermind, found it... In that paper he even quotes Eckmann's paper to say that corestriction $\textit{on cohomology groups}$ is independent of transversals. But from what I get from glancing at the paper, Choi looks at a certain map $p$ on the cochains which induces the corestriction map on cohomology groups, and this map $p$ has different values at the cochain-level dependent on transversals. –  Chris Gerig Mar 13 '11 at 9:00