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Stiefel–Whitney class

{c}
{title2=$w(T\mathbb P(k\gamma_{\mathbb R}^{1,n+1}))$}

Under
$$
\mathbb P(k\gamma_{\mathbb R}^{1,n+1})
\cong\mathbb{RP}^n\times\mathbb{RP}^{k-1},
$$
let $x$ and $v$ be the degree-one generators. Then
$$
w(T\mathbb P(k\gamma_{\mathbb R}^{1,n+1}))
=(1+x)^{n+1}(1+v)^k.
$$


Total Stiefel–Whitney class of the projectivization of copies of the tautological line

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 142 / 1 / Solution

Total Stiefel–Whitney class of the projectivization of copies of the tautological line ( $w (T P (k γ_{R}^{1, n + 1}))$ )

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Total Stiefel–Whitney class of the projectivization of copies of the tautological line (w(TP(kγR1,n+1​)))

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Total Stiefel–Whitney class of the projectivization of copies of the tautological line ( $w (T P (k γ_{R}^{1, n + 1}))$ )

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