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I have split off complex projective space from projective space and added some basic facts about its cohomology.
I have added a bunch of basic stuff to complex projective space:
the definition with some more details;
the statement and proof of the standard cell structure;
the statement and proof of the ordinary homology groups and cohomology rings;
the statement and proof of the complex oriented cohomology ring
(the last one essentially copied over from complex oriented cohomology theory, for completeness).
Sure! Please do.
Since it was missing, I have added statement and proof of the homotopy groups of $\mathbb{C}P^n$ (now here).
In doing so, I noticed that an existing Properties-section titled “Homotopy” really should have been titled “Relation to topological K-theory”, so I renamed it and also moved it further down the list (to have the Properties ordered, roughly, from more basic to more sophisticated), now here
added the statement (here) that $\mathbb{C}P^n$ is an Oka manifold
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