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Results tagged with cohomology
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user 3901
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, ...
44
votes
4
answers
5k
views
Integral cohomology (stable) operations
There have been a couple questions on MO, and elsewhere, that have made me curious about integral or rational cohomology operations. … So my questions are essentially as follows:
1) Are there any "interesting" rational cohomology operations? …
- 9,263
5
votes
Formal Group Laws on Ring Spectra?
I think the right correspondence is the one mentioned in the comments.
The main reason is that if you have a map of ring spectra $HL \to E$ then $E$ is an Eilenberg-Maclane spectrum. So in particular, …
- 3,726
4
votes
Are the homology and cohomology Serre spectral sequences dual to each other?
What is true though, is that if X is an H-space, then the differential in the homology Serre SS is a derivation like it is in cohomology. …
- 3,726
11
votes
Accepted
Examples of computing Ext and Tor functors?
$\mathbb{Q}/\mathbb{Z}$ is a pretty terrible abelian group, or a rather hard one, there may be better injective resolutions to work with. It would certainly be easier to do the projective resolution, …
- 3,726
15
votes
1
answer
1k
views
Complex orientations on homotopy
I am wondering if there is a more "geometric" formulation of complex orientations for cohomology theories than just a computation of $E^*\mathbb{C}$P$^{\infty}$ or a statement about Thom classes. … how much of these $E$-orientations of X is detected by E-cohomology of X? …
- 3,726