Abstract
Recent papers have discussed digital versions of the classical fundamental group for digital images. It has been shown that for non-contractible digital simple closed curves, the digital fundamental group is isomorphic to the integers, in analogy with Euclidean simple closed curves. In this paper, we show that the digital fundamental groups of sphere-like digital images S n , n > 1, are trivial, as are the fundamental groups of their Euclidean analogs Sn.
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Research partially supported by a grant from the Niagara University Research Council.
Laurence Boxer is Professor and past Chair of Computer and Information Sciences at Niagara University, and Research Professor of Computer Science and Engineering at the State University of New York at Buffalo. He received his Bachelor's degree in Mathematics from the University of Michigan; Master's and PhD in Mathematics from the University of Illinois at Urbana-Champaign; and Master's in Computer Science from the State University of New York at Buffalo. Dr. Boxer is coauthor of Algorithms Sequential and Parallel, an innovative textbook published by Charles River Media.
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Boxer, L. Homotopy Properties of Sphere-Like Digital Images. J Math Imaging Vis 24, 167–175 (2006). https://doi.org/10.1007/s10851-005-3619-x
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DOI: https://doi.org/10.1007/s10851-005-3619-x