On the first pontrjagin class of homotopy complex projective spaces

Abstract

ABSTRACT. Let 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.