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Results tagged with cohomology
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user 102515
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, ...
13
votes
1
answer
882
views
Cohomology of $ko,tmf,MSpin,MString$ with coefficients $\mathbb{Z}/p$ for odd primes $p$
It is well-known that $$H^*(ko,\mathbb{Z}/2)=\mathcal{A}\otimes_{\mathcal{A}(1)}\mathbb{Z}/2$$
$$H^*(tmf,\mathbb{Z}/2)=\mathcal{A}\otimes_{\mathcal{A}(2)}\mathbb{Z}/2$$
where $\mathcal{A}$ is the mod …
- 1,329
8
votes
0
answers
270
views
Generalize Wu formula to general Bockstein homomorphisms
The classical Wu formula claims that
$$Sq^1(x_{d-1})=w_1(TM)\cup x_{d-1}$$
on a $d$-manifold $M$, where $x_{d-1}\in H^{d-1}(M,\mathbb{Z}_2)$.
I wonder whether there is a generalization of the classic …
- 1,329
18
votes
1
answer
1k
views
Wu formula for manifolds with boundary
smooth closed $n$-manifold with fundamental class $z\in H_n(M;\mathbb{Z}_2)$, then the total Stiefel-Whitney class $w(M)$ is equal to $Sq(v)$, where $v=\sum v_i\in H^*(M;\mathbb{Z}_2)$ is the unique cohomology …
- 1,329