摘要
设(M,T)是一个带有光滑对合T的光滑闭流形,T在M上的不动点集为F={x|T(x)=x,x∈M}.则F为M的闭子流形的不交并.
本文讨论了:
(1)当F=P(2m,2l+1)(?)P(2m,2n+1)时,其中n>l≥m,m≠1,3,(M,T)协边于零.
(2)当F=P(2~m,2~m)(?)P(2~m,2~m+1),且m≥3时,完全决定了带有对合的流形(M,T)的等变协边分类.
Let(M,T)be a smooth closed manifold with a smooth involution Twhose fixed point set is F={x|T(x)=x,x∈M},then F is the disjoint union ofsmooth closed submaniflod of M.
In this paper,we discuss:
(1) For F=P(2m,2l+1)(?)P(2m,2n+1),n>l≥m,m≠1,3,them(M,T)isbounded.
(2) For F=P(2~m,2~m)(?)P(2~m,2~(m)+1),m≥3,the all bordism classes of(M,T)are decided.
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