  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.
