具有(Z_2)~k作用不动点集为{p}∪V^(4m+2)的光滑闭流形

The Smooth Closed Manifold with {p}∪V^( 4m+2)Being the Fixed Point Set of(Z_2)~k-action

设 (Mr ,Φ)是 r维光滑闭流形 Mr上的 (Z2 ) k作用 ,其不动点集为 {p}∪ V4 m+ 2 ,且 V4 m+ 2～2 CP(2 m+1 ) .研究了流形 Mr的维数和 (Mr,Φ)的等价协边类 ,得到如下结论1) r=(4 m+4) 2 t- 1 ,t为某整数且 1≤t≤k;2 ) [Mr ,Φ]2 =[σΓkt(CP(2 m+2 ) ,τ0 ) ]2 .

Suppose( M r,Φ )is a differientiable( Z 2) k action on an r dimensional closed manifold M r with the fixed point set of Φ being the disjoint union of a point and a fixed connect (4m+2 ) dimensional manifold,that is, {p}∪V 4m+2 ,where V 4m+2 satisfies V 4m+2 ～2CP(2m+1) .The dimension of M r and the equivariant bordism class of( M r,Φ )are determined.The conleusion is obtained: 1) r=(4m+4)2 t-1 for some integer t,1≤t≤k; 2) 2=[σΓ k t(CP(2m+2),τ 0)] 2.