THE PONTRJAGIN CLASS OF A HOMOTOPY COMPLEX PROJECTIVE-SPACE

We develop a formula for the Pontrjagin class of a PL homotopy complex projective n-space and offer two applications. If n = 4, 5, or 6, we characterize the Pontrjagin classes of those PL homotopy complex projective n-spaces which admit a locally linear PL Z3-action with a codimension-2 fixed submanifold. If n is odd and n ≥ 5, we show that there are infinitely many PL homotopy complex projective n-spaces with no compatible differentiable structure and integral Pontrjagin class. © 1990.