Digital Homotopy with Obstacles

✍ Scribed by R. Ayala; E. Domínguez; A.R. Francés; A. Quintero

• Book ID: 104445158
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 287 KB
• Volume: 46
• Category: Article
• ISSN: 1571-0661
• DOI: 10.1016/s1571-0661(04)80980-0

✦ Synopsis

As a sequel of [4], 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 for arbitrary digital spaces the group π d 1 (O/S; σ) maps onto the usual fundamental group of the difference of continuous analogues |A O∪S | -|A S |. 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.