A digital index theorem

This paper is devoted to state and prove a Digital Index Theorem for digita l (n-1)-manifolds in a digital space (R-n, f), where f belongs to a large f amily of lighting functions on the standard cubical decomposition R-n of th e n-dimensional Euclidean space. As an immediate consequence we obtain the corresponding theorems for all (alpha,beta)-surfaces of Kong-Roscoe, with a lpha, beta is an element of { 6, 18, 26} and (alpha,beta) not equal (6, 6), (18, 26), (26, 26), as well as for the strong 26-surfaces of Bertrand-Malg ouyres.