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nLab > Latest Changes: complex projective space

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 15th 2016

    I have split off complex projective space from projective space and added some basic facts about its cohomology.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 10th 2016
    • (edited May 10th 2016)

    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).

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 6th 2020

    added brief mentioning of the Sullivan model of ℂP n\mathbb{C}P^n

    diff, v28, current

    • CommentRowNumber4.
    • CommentAuthorEgbertRijke
    • CommentTimeAug 6th 2020
    I can write something about its definition in HoTT, if that is appropriate on this page
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 6th 2020

    Sure! Please do.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 27th 2021
    • (edited Jan 27th 2021)

    Since it was missing, I have added statement and proof of the homotopy groups of ℂP n\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

    diff, v35, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 17th 2021

    added the statement (here) that ℂP n\mathbb{C}P^n is an Oka manifold

    diff, v36, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeAug 17th 2021

    added pointer to:

    diff, v39, current

    • CommentRowNumber9.
    • CommentAuthorSamuel Adrian Antz
    • CommentTimeFeb 5th 2024
    • (edited Feb 5th 2024)

    Added fixed-point property for complex projective space.(The general subsection of properties already existed, but was empty so far.) Also added Hatcher as a reference.

    (Also there seems to have been a little glitch, that previously replacing “is” by “are” was taken into the log twice with only a difference of five seconds inbetween. I’ve submitted it without comment.)

    diff, v48, current

  10. Added topological complexity (for which I intend to create a page in the future) of complex projective space.

    diff, v50, current

    • CommentRowNumber11.
    • CommentAuthorSamuel Adrian Antz
    • CommentTimeFeb 8th 2024
    • (edited Feb 8th 2024)

    Added topological complexity (for which I intend to create a page in the future) of complex projective space.

    (The glitch appeared again and the edit is now in the log twice with a time difference of only two seconds.)

    diff, v50, current

1 to 11 of 11

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