Digital Homotopy with Obstacles

Abstract

As a sequel of [4], this paper is devoted to the computation of the digital fundamental group πd1(O/S;σ) defined by loops in the digital object O for which the digital object S acts as an “obstacle”. We prove that for arbitrary digital spaces the group πd1(O/S;σ) maps onto the usual fundamental group of the difference of continuous analogues ∣ AO∪S∣ − ∣ AS∣. Moreover, we show that this epimorphism turns to be an isomorphism for a large class of digital spaces including most of the examples in digital topology.