一个有关光滑对合的定理

A Theorem About a Manifold with Involution

旨在证明以下定理:设(Mn,T)是一个在n维闭光滑流形上的光滑对合,并且Sω[M]≠0;及ω=(1,…,1),|ω|=n则对于对合的不动点集来说其法丛的维数至多是n/2.

Let (n.T) be a differentiable involution on a closed manifold. If the S_ω[M]≠0 and ω=(1,…,1),｜ω｜=n, then the dimension of normal bundle over the component of fixed point set equals or less than n/2.