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2016•Unpublished venueRequires access

HOMOTOPY EQUIVALENCE IN FINITE DIGITAL IMAGES

Jason Haarmann, Meg P. Murphy, Casey S. Peters, P. Christopher Staecker

Open publisher page 22 citations

Abstract

For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain invariants in the digital setting. This paper develops a numerical digital homotopy invariant and begins to catalog all possible connected digital images on a small number of points, up to homotopy equivalence.

About this research paper

What this paper is about

For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain invariants in the digital setting. This paper develops a numerical digital homotopy invariant and begins to catalog all possible connected digital images on a small number of points, up to homotopy equivalence.

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OpenAlex reports 22 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain invariants in the digital setting. This paper develops a numerical digital homotopy invariant and begins to catalog all possible connected digital images on a small number of points, up to homotopy equivalence.

Key concepts: Homotopy, Mathematics, n-connected, Homotopy sphere, Regular homotopy, Equivalence (formal languages), Euler characteristic, Homotopy lifting property

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