FRANCÉS ROMÁN , Ángel Ramón

The main contribution of this paper is a new "extrinsic" digital fundamental group that can be readily generalized to define higher homotopy groups for arbitrary digital spaces. We show that the digital fundamental group of a digital object is naturally isomorphic to the fundamental group of its continuous analogue. In addition, we state a...

For each adjacency pair (k, k) != (6, 6), k, k ∈ {6, 18, 26}, we introduce a new family Skk of surfaces in the discrete space Z3 that strictly contains several families of surfaces previously defined, and other objects considered as surfaces, in the literature. Actually, Skk characterizes the strongly k−separating objects of the family of...

This paper is devoted to prove a Digital Index Theorem for digital (n − 1)-manifolds in a digital space (Rn, f), where f belongs to a large family of lighting functions on the standard cubical decomposition Rn of the n-dimensional Euclidean space. As an immediate consequence we obtain the corresponding theorems for all (α, β)-surfaces of...

As a sequel of [4] Ayala, R., E. Dom´ıguez, A. R. Franc´es and A. Quintero, Homotopy in Digital Spaces, Discrete and Applied Mathematics, To Appear, this paper is devoted to the computation of the digital fundamental group π d 1 (O/S; σ) defined by loops in the digital object O for which the digital object S acts as an "obstacle". We prove that...

In R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, J. Rubio. A Polyhedral Approach to Digital Topology a new framework for digital topology has been proposed. This framework offers the possibility of transfering, in an easy way, definitions, statements and proofs from continuous topology to digital topology. In particular, it provides a...