Involutions With Fixed Point Set P(5 ,2l+1) UP(5,2n+1)

Let(M,T)be a smooth closed manifold with a smooth involution T whose fixed point set is F={x| T(x)=x,x∈M},then F is the disjoint union of smooth closed submanifold of M.In this paper,we discuss the involutions fixing the Dold manifold or the disjoint union of Dold manifolds.(1) For F=P(5,2n+1),n>2,(n2)=0(mod2),k>0 and k≠2,then the involution (M4n+7+k,T) is bounded；(2) For F=P(2m+1,2n+1),2m+2n=2+22+…+2b,2b is the biggest power of 2 of the dyadic expression of 2n,k>0 and k≠2,then the involution(M4n+2m+3+k,T) is bounded;(3) For F=P(5,2l+1)u P(5,2n+1),n>2>2 and k>10,then the involution (M4n+7+k,T) is bounded;(4) For F=P(2m+1,2l+1)(?) P(2m+1,2n+1),n>l≥m≥3 and k>4m+2, then the involution(M4n+2m+3+k,T)is bounded.