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Results tagged with cohomology
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user 126407
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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Order relation between cohomology groups
We have $\mathbb{Q}$-graded finite dimensional vector space $V=\bigoplus_{i=0}^{n}V_{i}$ and following cochain complex
$$0\rightarrow V_{0}\xrightarrow[]{d_{0}} V_{1}\xrightarrow[]{d_{1}}\ldots\xrigh …
- 173
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Relation between cohomological dimensions of manifolds
$\DeclareMathOperator\Ch{Ch}$Let $M$ be a connected manifold of finite type. We denote $\Ch_{\mathbb{Q}}(M),$ $\Ch_{\mathbb{Z}}(M)$ and $\Ch_{\mathbb{\pm}\mathbb{Z}}(M)$ by cohomological dimensions of …
- 173