不动点集为 Dold 流形 P（2,1）的对合

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。本文证明了：当 F=P(2,1)时，(M,T)协边于零。%Let (M,T) be a smooth closed manifold with a smooth involution T whose fixed point set is F={x|T(x)=x, x∈M}, then F is the disjoint union of smooth closed submanifold of M. In this paper, we prove: for F=P(2,1), then (M ,T) is bounded.