不动点集为Dold流形P(2,1)的对合

Involutions Fixing the Dold Manifold P(2, 1)

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.