The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms of Euler characteristic in the case of closed manifolds, where we give a new proof of w_m(G)=w_1(G). Also the sphere formula generalizes: for any simplicial complex, the total higher characteristics of unit spheres at even dimensional simplices is equal to the total higher characteristic of unit spheres at odd dimensional simplices.

翻译：对于有限抽象单纯复形G的高次特征w_m(G)是满足k点格林函数恒等式的拓扑不变量，在闭流形情形下可通过欧拉示性数计算，本文给出了w_m(G)=w_1(G)的新证明。球面公式也得到了推广：对于任意单纯复形，偶数维单形处单位球面的总高次特征等于奇数维单形处单位球面的总高次特征。