(of corresponding dimensions). how can I prove this? I think my main stumbling block is my general ignorance of group cohomology.
integral cohomology groups of an aspherical manifold are isomorphic to the integral cohomology groups of it's fundemental group
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algebraic-topology
commutative-algebra
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2To answer this, we need to know what is your definition of group cohomology. – 2012-01-05
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0I have only learned the definition contained in Dummit and Foote wherein it is defined to be $Ext_{\mathbb{Z}G}(\mathbb{Z},\mathbb{Z})$. Are there non-equivalent definitions? – 2012-01-05
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1All definitions are equivalent, but to prove something is equivalent to one of them you need to actually pick one of them! – 2012-01-05
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2By the way, it is usually best if the body of the question is self contained and, in particular, does not require the title to make sense (your titiel/question does not satisfy this condition): have you ever seen a book whose first sentence starts in the cover? – 2012-01-05
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0agreed! though I'm willing to work out the equivalence between your definition and mine if yours lends itself to a proof of the statement. – 2012-01-05