以{p}∪F^(4m+2)为不动点集的光滑对合

The Closed Manifold with{p}∪F^(4m+2) Being the Fixed Point Set of a Smooth Involution

设 (Mn,T)是n维光滑闭流形Mn 上以 { p} ∪F4m +2 为不动点集的对合 ,其中F4m +2 ～2CP( 2m+1) ,确定了流形Mn 的维数并给出 (Mn,T)的等价协边类 ,即 [Mn,T]2 =[CP( 2m +2 ) ,τ0 ]2 ,且n=4m +4.

Suppose (Mn,T) is a differientiable involution on an n-dimensional closed manifold Mn with the fixed point set of T being the disjoint union of a point and a fixed connect (4m+2)-dimensional manifold,that is {p}∪F 4m+2,where F 4m+2 satisfies F 4m+2～2CP(2m+1).The dimension of Mn is determinecl and the the equivariant bordism class of(Mn,T) is given,i.e,n=4m+4 and 2=[CP(2m+2),τ 0] 2.