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Results tagged with cohomology
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user 43639
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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Is there an analogue of CW-complexes built from $K(\mathbb Z, n)$ instead of $S^n$?
From them we can build $n$-th homotopy groups $\pi_n(X):=[S^n, X]$ and $n$-th (integral) cohomology groups $H^n(X):=[X, K(\mathbb Z, n)]$, where $[A, B]$ means a set of homotopy classes of maps from $A … case would be if one can dualize any statement about CW-complexes and get a true statement about objects in this category, and if it contains spheres and $K(\mathbb Z, n)$, so that we have homotopy and cohomology …
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