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Results tagged with cohomology
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user 148857
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, ...
15
votes
Accepted
When homology isomorphism implies homotopy isomorphism
Here's a counterexample.
Set $X'=S^1\vee S^2$.
Consider the following map $F':S^2\vee S^2\vee S^2\rightarrow X'$: It maps the first $S^2$ summand to the $S^2$ summand of $X'$ via a map that repres …
- 1,150
1
vote
Accepted
Chern classes of complex vector bundle
You'll have to use cohomology over $\mathbb{Z}/2$ and you'll be calculating Stiefel-Whitney classes instead of chern classes, but the procedure is exactly the same: Leray-Hirsch, read off coefficients … Then $P(E)$ will be a familiar non-orientable surface (Klein bottle) whose cohomology ring you can compute from a delta-decomposition. …
- 1,150