A digital index theorem
This paper is devoted to state and prove a Digital Index Theorem for digital (n-1)-manifolds in a digital space (R-n, f), where f belongs to a large family of lighting functions on the standard cubical decomposition R-n of the n-dimensional Euclidean space. As an immediate consequence we obtain the corresponding theorems for all (alpha,beta)-surfaces of Kong-Roscoe, with alpha, 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-Malgouyres.
index theorem weak lighting functions digital n-manifold