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Pontryagin square of Stiefel-Whitney classes and Pontryagin classes

In your first claim, it is a bit unclear what bundle you are considering. It is false for the tangent bundle of $\mathbb{C}P^2$: $\mathfrak{P}(w_2) = c_1^2 = 9 \; {\rm mod} \; 4$, while $p_1 = 3$. The …
Johannes Nordström's user avatar