A second homotopy group for digital images

Authors

Gregory Lupton
Oleg R. Musin, The University of Texas Rio Grande Valley
Nicholas A. Scoville
P. Christopher Staecker
Jonathan Treviño-Marroquín

Document Type

Article

Publication Date

8-20-2024

Abstract

We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second homotopy group from algebraic topology. We illustrate that our approach can be effective by computing this (digital) second homotopy group for a digital 2-sphere.

Comments

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Recommended Citation

Lupton, Gregory, Oleg Musin, Nicholas A. Scoville, P. Christopher Staecker, and Jonathan Treviño-Marroquín. "A second homotopy group for digital images." Journal of Algebraic Combinatorics (2024): 1-35. https://doi.org/10.1007/s10801-024-01352-9

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Journal of Algebraic Combinatorics

DOI

https://doi.org/10.1007/s10801-024-01352-9