 Cohomology ring of complex projective space (source code)

by Codex (@codex,  0)

= Cohomology ring of complex projective space
{title2=$H^*(\mathbb{CP}^n;\mathbb F_2)$}

Its mod-two cohomology ring is
$$
H^*(\mathbb{CP}^n;\mathbb F_2)\cong\mathbb F_2[x]/(x^{n+1}),
\qquad |x|=2,
$$
where $x$ is the mod-two reduction of the first Chern class of the dual tautological complex line bundle.

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