homotopy complex
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On the first pontrjagin class of homotopy complex projective spaces

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Yasuhiko Kitada
Keyword(s):  
Projective Space ◽  
Smooth Manifold ◽  
Complex Projective Space ◽  
Projective Spaces ◽  
Homotopy Equivalent ◽  
Complex Projective Spaces ◽  
Pontrjagin Class ◽  
Complex Projective ◽  
Homotopy Complex

AbstractLet M 2n be a closed smooth manifold homotopy equivalent to the complex projective space ℂP(n). It is known that the first Pontrjagin class p 1(M) of M 2n has the form (n+1+24α(M))u 2 for some integer α(M) where u is a generator of H 2(M; ℤ). We prove that α(M) is even when n is even but not divisible by 64.

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