Kunneth formula for group cohomology: Difference between revisions

Latest revision as of 05:30, 22 September 2015

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+{{quotation|'''The details of the page have been blanked out due to a notification about an error in the statement; see [http://mathoverflow.net/questions/75472/kuenneth-formula-for-group-cohomology-with-nontrivial-action-on-the-coefficient Math Overflow for more].'''}}
 ==Statement==
 ===For trivial group action===
-Suppose <math>G_1,G_2</math> are [[group]]s and <math>A</math> is an [[abelian group]]. We have the following formula for the [[fact about::cohomology group for trivial group action;1| ]][[cohomology group for trivial group action|cohomology groups for trivial group action]] of <math>G_1 \times G_2</math> on <matH>A</math> in terms of the [[cohomology group for trivial group action|cohomology groups for trivial group action]] of <math>G_1</math> and <math>G_2</math> respectively on <matH>A</math>:
+{{fillin}}
-<math>H^n(G_1 \times G_2; A) \cong \left(\sum_{i+j = n} H^i(G_1;A) \otimes H^j(G_2;A) \right) \oplus \left(\sum_{p + q = n + 1} \operatorname{Tor}^1_{\mathbb{Z}}(H^p(G_1;A),H^q(G_2;A)\right)</math>
 ===For nontrivial group action===