Cohomology Complex Projective Space with Actions of G_5

摘要

Let M2n be a cohomology CPn and p a prime. S et Dp(M2n)={d＞0|M2n admits a smooth Gp action such tha t the fixed point set of the action contains a codimension-2 submanifold of deg ree d}, DEp(M2n)={(d; m1, m2, …, mμ)|M2n admits a GP action of Type Ⅱ0, having multiplicities m1, m2, …, mμ at the isolated fixed points, and m1+m2+…+mμ=n, d is the degree of the fixed codimension-2 submanifold}. In this paper, we prove that for n=5 or 7 , if D5(M2n)≠φ, then D5(M2n)={1}; if DE5(M2n )≠φ, then DE5(M2n)={(1; n, 0)}.