带有n个洞的圆盘上扭转微分同胚的不动点数

The number of fixed points of twist diffeomophism on disk with n holes

利用球面上光滑向量场的奇点指标定理(Poincar啨-Hopf定理),给出了带有n个洞的圆盘上扭转微分同胚的不动点数估计及辛同胚情形不动点个数的下界限制.对于辛微分同胚给出了Poincar啨几何定理的一个直观证明.

By using poincaré-Hopf index theorem, we present an estimate of the number of fixed points of twist diffeomorphism on a disk with n holes. At same time, A new proof was given to Poincaré geometry theorem at the case of sympletic diffeomprphism.