具有不动点集*∪F^(4l+2)的可换对合

THE COMMUTING INVOLUTION WITH * ∪F^(4L+2) BEING THE FIXED POINT SET

设(M',Φ)是r维光滑闭流形M'上的(Z2)k作用,其不动点集为*∪F4l+2,且F4l+2～CP(2l+1).本文研究流形M'的维数和(M',Φ)的等价协边类,得到结论: (1)r=(4l+4)·2t-1,t为整数,且1≤t≤k; (2)[M,Φ]2=[σГtk(CP(2l+2),τ0)]2.

Suppose (Mr,Φ) is a differientiable (Z2)k-action on a r-dimensional closed manifold AT with the fixed point set of Φ being the disjoint union of a single point and a fixed connect (4l + 2)-dimensional manifold, that is * ∪F4l+2 satisfies F4l+2-CP(2l + 1). In this paper, it determines the dimension of Mr and the equivariant bordism class of (Mr ,Φ). In conclusion, it has: (1) r=(4l + 4)2t-1 for some integer t,1≤t≤k; (2)[M,Φ]2=[σГtk(CP(2l+2),τ0)]2.