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Results tagged with steenrod-algebra
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user 8103
10
votes
Accepted
Why does $\iota_4^2 \in H^8(K(\mathbb Z/2,4);\mathbb Z/2)$ not come from $H^8(K(\mathbb Z/2,...
It is true, and follows from results of Browder on the mod 2 Bockstein spectral sequence for $K(\mathbb{Z}/2,4)$. (We can replace $4$ by any even integer $k$ and conclude that $\iota_k^2$ ia not the r …
- 35.9k
3
votes
Steenrod operations in algebraic geometry
You may be interested in the thesis of Olivier Haution, entitled Steenrod operations and quadratic forms. The author gives a new approach to constructing Steenrod operations on the Chow ring mod p, an …
- 35.9k
5
votes
Bockstein homomorphism and Square Operations: Their consistency formulas
I'm not sure if this is what you are asking, but you get useful relations among the Bockstein operators whenever you have a map between short exact coefficient sequences. For example, using the map of …
- 35.9k
11
votes
Accepted
Steenrod operations on cohomology of grassmannians
As in Prasit's comment, the action of the Steenrod squares on the Stiefel-Whitney classes of any vector bundle are given by Wu's formula
$$
Sq^i(w_j) = \sum_{t=0}^i \binom{j+t-i-1}{t} w_{i-t} w_{j+t}. …
- 35.9k
7
votes
Pontryagin square, Postnikov square and their consistency formulas
You may be interested in the following paper:
Massey, W. S., Pontryagin squares in the Thom space of a bundle, Pac. J. Math. 31, 133-142 (1969). ZBL0188.28504.
Massey proves an analogue for the Pont …
- 35.9k