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Projective Space

  1. Oct 9, 2008 #1
    I have a question about complex projective space... specifically CP1 which can be thought of as the action of C on C^2\{0} which gives rise to the equivalence classes of "lines" passing through the origin in C^2 (but not including the 0) Now, any vector in complex space, when multiplied by the set of all complex numbers of a given norm will give rise to a circle...and in a sense, when C (numbers of all norm!) acts of C^2 you simply get equivalence classes of planes... I think anyway..someone correct me if I am wrong...but the ultimate question is.. is this homeomorphic to a 2 sphere?
    Last edited: Oct 9, 2008
  2. jcsd
  3. Oct 11, 2008 #2
    Yes, CP1 is the 2-sphere. This construction of S2 from C2 is on way to do the celibrated Hopf fibration.
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