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

ID: total-stiefel-whitney-class-of-the-projectivization-of-copies-of-the-tautological-line

Under

P (k γ_{R}^{1, n + 1}) ≅ RP^{n} \times RP^{k - 1},

let

x

and

v

be the degree-one generators. Then

w (T P (k γ_{R}^{1, n + 1})) = (1 + x)^{n + 1} (1 + v)^{k} .

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