Cyclic actions and divisible polynomials

Let g:M2nlong right arrowM2n be an orientation preserving PL map of period m>2. Suppose that the cyclic action defined by g is locally linear PL, fixing a locally flat submanifold F with components only of dimension 0 or 2n−2, and regular. Let phi(m) be Euler’s number and ρ(m)=phi(m)−1 if m is a power of 2 and ρ(m)=phi(m) otherwise. If image is a rational integer, then image. This congruence is used to show that a codimension-2 locally flat submanifold of cohomology complex projective n-space fixed by g must have degree one if m≠4 or 10 and n