The first Pontrjagin classes of homotopy complex projective spaces

Abstract

Let $M^{2n}$ be a closed smooth manifold homotopy equivalent to the complex projective space $\mathbb{C}P(n)$. The purpose of this paper is to show that when $n$ is even, the difference of the first Pontrjagin classes between $M^{2n}$ and $\mathbb{C}P(n)$ is divisible by 16.