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.
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R. Ayala, E. Domínguez, A. R. Francés, A. Quintero. Digital Lighting Functions. Lecture Notes in Computer Science. 1347(1997) 139–150. 4, 6, 8, 12
R. Ayala, E. Domínguez, A. R. Francés, A. Quintero. Weak lighting functions and strong 26-surfaces. To appear in Theoretical Computer Science. 4
E. Khalimsky. Motion, deformation and homotopy in finite spaces. Proc. of the 1987 IEEE Int. Conf. on Systems., Man and Cybernetics, 87CH2503-1. (1987) 227–234. 3, 13
T. Y. Kong. A Digital Fundamental Group. Comput. & Graphics, 13(2). (1989) 159–166. 3, 13
R. Malgouyres. Homotopy in 2-dimensional digital images. Lecture Notes in Computer Science. 1347(1997) 213–222.
R. Malgouyres. Presentation of the fundamental group in digital surfaces. Lecture Notes in Computer Science. 1568(1999) 136–150.
R. Malgouyres. Computing the fundamental group in digital spaces. Proc. of the 7th Int. Workshop on Combinatorial Image Analysis IWCIA’00. (2000) 103–115. 4
C. R. F. Maunder. Algebraic Topology. Cambridge University Press. 1980. 4
J. R. Munkres. Elements of algebraic topology. Addison-Wesley. 1984. 10
J. J. Rotman. An introuduction to algebraic topology. GTM, 119. Springer. 1988. 12
J. Stillwell. Classical topology and combinatorial group theory. Springer. 1995. 3
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Ayala, R., Domínguez, E., Francés, A.R., Quintero, A. (2000). Homotopy in Digital Spaces. In: Borgefors, G., Nyström, I., di Baja, G.S. (eds) Discrete Geometry for Computer Imagery. DGCI 2000. Lecture Notes in Computer Science, vol 1953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44438-6_1
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DOI: https://doi.org/10.1007/3-540-44438-6_1
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