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Results tagged with cohomology
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user 132128
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, ...
7
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1
answer
501
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Topology of connected subsets of the $3$-torus
I am concerned with the subsets
$$ A = \ker (H^1(Y)\to H^1(\Sigma)), \quad B=\ker (H^1(Y)\to H^1(\Sigma^*))$$
of the first de Rham cohomology of $Y$. The maps are induced by the restriction maps. …
- 181
1
vote
Topology of connected subsets of the $3$-torus
The following is my own attempt at an answer. I would appreciate critical proofreading.
The exact sequences of the pairs $(Y,\Sigma)$ and $(Y,\Sigma^*)$ show that
$$
A=\operatorname{im}(i^*:H^1(Y,\Si …
- 181