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Results tagged with cohomology
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user 4625
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, ...
10
votes
How are these algebraic and geometric notions of homotopy of maps between manifolds related?
It's very hard to go back since an algebraic homotopy is very weak information, it exists if and only if $f$ and $g$ induce the same map on de Rham cohomology (since these are chain complexes over a field …
- 1,696
7
votes
Accepted
Is the following map from Z(G) x H^3(G, C*) --> H^2(G, C*) ever nontrivial?
The proof is easy since the cohomology rings are polynomial, respectively exterior, algebras. …
- 1,696
21
votes
Accepted
Complex orientations on homotopy
For example, if E=HZ is ordinary Z-cohomology then X=BSO works, if E=KO then X=BSpin works, if E=KU then X=BU or X=BSpin$^c$ works etc. … In the case X=BU this is called a complex orientation of E and has been studied extensively because it simplifies computations of E-cohomology tremendously. …
- 1,696
18
votes
Explanation for the Chern character
The hard part is to explain why domain and range of this map are K-theory respectively de Rham cohomology. …
- 1,696