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

10-2023

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.

Recommended Citation

Lupton, Gregory, Oleg Musin, Nicholas A. Scoville, and P. Treviño-Marroquín. "A Second Homotopy Group for Digital Images." arXiv preprint arXiv:2310.08706 (2023).