带边流形上向量场的奇点指标公式及其应用

An Index Formula of Singularities of Vector Fields on Manifolds with Boundary and Its Application

讨论了M .Morse关于带边流形上向量场的奇点指标公式 ,应用延拓形变成adapted场的方法 ,给出了该公式一个更为简洁本质的证明 ,得到Rn 中单连通区域上连续映射的孤立零点估计 .它可以被看成是辐角原理的一般推广 .

An index formula of singularities of vector fields on manifolds with boundary due to M.Morse was discussed. By using the method of deformation and extended to adapted fields, we get a more precise and essential proof of this index formula.As an appliction of it, an estimate of isolated zeros of continuous mapping on simply connected domain is obtained. It can be considered as a generalized version of the classical arguement principle.