Homotopy Properties of Sphere-Like Digital Images

Author: Boxer, Laurence¹

Source: Journal of Mathematical Imaging and Vision, Volume 24, Number 2, March 2006 , pp. 167-175(9)

Publisher: Springer

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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.

Keywords: digital image; digitally continuous; homotopy; fundamental group; digital topology

Document Type: Research article

DOI: 10.1007/s10851-005-3619-x

Affiliations: 1: Email: boxer@niagara.edu

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