most recent 30 from http://mathoverflow.net 2013-05-21T02:22:26Z http://mathoverflow.net/feeds/question/58279 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58279/corestriction-and-transversals Esther Beneish 2011-03-12T18:25:12Z 2011-03-16T21:31:43Z

<p>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? </p>

http://mathoverflow.net/questions/58279/corestriction-and-transversals/58281#58281 Chris Gerig 2011-03-12T19:08:50Z 2011-03-16T21:31:43Z

<p>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.</p> <p>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.</p>