Involutions Fixing F=P(2m₁, 2n+1)UP(2m₂, 2n+1)

Let(M,T)be a smooth closed manifold with a smooth involution T:M→M whose fixed point set is F={x｜T(x)=x,x∈M}.In this paper,we discuss the involutions fixing the Dold manifold and it's disjoint union.(1) For F=P(2m1,2n+1)(?)P(2m2,2n+1),(4≤m1<m2≤n,m1=1,2,3 and m2≠3),in some cases,(M,T)is bounded.(2) For F=(?) P(2mi,2n+1)(mi≥4,l≥3)(n≥ml>…>m1≥4),(M,T)is bounded.(3) For F=P(2,2n+1),we consider two special cases:F=P(2,1) and F= P(2,3).In these cases,(M,T)are bounded.