Homotopy in digital spaces

Authors:
R. Ayala;E. Domínguez;A. R. Francés;A. Quintero
Affiliations:
Departamento de Geometría y Topología, Facultad de Matemàticas, Universidad de Sevilla, Apto. 1160, E-41080 Sevilla, Spain;Departamento de Informática e Ingeniería de Sistemas, Facultad de Ciencias, Universidad de Zaragoza, E-50009 Zaragoza, Spain;Departamento de Informática e Ingeniería de Sistemas, Facultad de Ciencias, Universidad de Zaragoza, E-50009 Zaragoza, Spain;Departamento de Geometría y Topología, Facultad de Matemàticas, Universidad de Sevilla, Apto. 1160, E-41080 Sevilla, Spain
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

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 digital version of the Seifert-Van Kampen theorem.