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Results tagged with steenrod-algebra
Search options questions only
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user 27004
5
votes
1
answer
251
views
Pontryagin square, Postnikov square and their consistency formulas
$\mathcal{P}_2$ is Pontryagin square
$$H^{2i}(M,\mathbb Z_{2^k})\to H^{4i}(M,\mathbb{Z}_{2^{k+1}}).$$
$\mathfrak{P}$ is the Postnikov square $$H^2(M,\mathbb Z_3)\to H^5(M,\mathbb Z_9).$$
questio …
- 10.5k
5
votes
0
answers
222
views
Generalizing the formula between Wu class and the Steenrod square
I know that on the tangent bundle of $M^d$, the corresponding Wu class and the Steenrod square satisfy
$$
Sq^{d-j}(x_j)=u_{d-j} x_j, \text{ for any } x_j \in H^j(M^d;\mathbb Z_2) .
\tag{eq.1}$$ …
- 10.5k
3
votes
1
answer
675
views
Bockstein homomorphism and Square Operations: Their consistency formulas
Here are various ways to define "Bockstein homomorphism:"
Let $\beta_p:H^*(-,\mathbb{Z}_p)
\to H^{*+1}(-,\mathbb{Z}_p)$ be the Bockstein homomorphism associated to the extension $$\mathbb{Z}_p\to\mat …
- 10.5k