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A branch of algebraic topology concerning the study of cocycles and coboundaries. It is in some sense a dual theory to homology theory. This tag can be further specialized by using it in conjunction with the tags group-cohomology, etale-cohomology, sheaf-cohomology, galois-cohomology, lie-algebra-cohomology, motivic-cohomology, equivariant-cohomology, ...

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How should one think about pushforward in cohomology?

It turns out that this description of ordinary $1$-cohomology generalizes in an elegant way to arbitrary dimensions and arbitrary cohomology theories, which was done in the B-R-S book. … $ in ordinary integral cohomology is defined for every representative $f$ of an ordinary cohomology class, that is for a co-oriented comanifold with codimension two singularities. …
Sergey Melikhov's user avatar