Certain topological methods for computing digital topological complexity

TL;DR

This paper explores the relationship between digital Lusternik-Schnirelmann category and digital higher topological complexity, introducing $ppa$-topological groups to deepen understanding of digital topological complexity with examples and counterexamples.

Contribution

It introduces $ppa$-topological groups in digital topology and investigates their role in understanding digital higher topological complexity, providing new insights and examples.

Findings

Relationships between digital Lusternik-Schnirelmann category and topological complexity clarified.

Introduction of $ppa$-topological groups offers a new perspective.

Examples and counterexamples illustrate the concepts effectively.

Abstract

In this paper, we examine the relations of two closely related concepts, the digital Lusternik-Schnirelmann category and the digital higher topological complexity, with each other in digital images. For some certain digital images, we introduce $\kappa-$topological groups in the digital topological manner for having stronger ideas about the digital higher topological complexity. Our aim is to improve the understanding of the digital higher topological complexity. We present examples and counterexamples for $\kappa-$topological groups.