Why no Almost complex structure on S^4

Discussion in 'Math Research' started by Alex, Jan 14, 2004.

  1. Alex

    Alex Guest

    It seems it's true that there is
    no almost complex structure on S^4.
    Why it is true ?
     
    Alex, Jan 14, 2004
    #1

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  2. Alex

    Shahram B. Guest

    in fact more is true: if X:=S^2n has an almost complex then n=1, 3. to
    show the latter, we know that as S^2n has an almost complex structure,
    the Euler and nth chern classes of the tangent bundle agree in H^2n(X,
    Z). however, the Euler class is exactly 2, whereas the nth chern class
    should divide (n-1)!.
     
    Shahram B., Jan 15, 2004
    #2

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