The first Pontrjagin classes of homotopy complex projective spaces

Let M2n be an oriented closed smooth manifold homotopy equivalent to the complex projective space CP(n). The main purpose of this paper is show that when n even, difference between first Pontrjagin class and CP(n) divisible by 16. As a geometric application result, we prove Kervaire sphere dimension 4k+1 does not admit any free circle group action if k+1 power 2.