Digital (co)homology modules and digital Pontryagin algebras

TL;DR

This paper investigates digital homology and cohomology modules, digital Hopf spaces, and digital Pontryagin algebras on digital images, extending algebraic topology concepts into digital topology.

Contribution

It introduces the concepts of digital Pontryagin algebras and explores their properties within digital Hopf spaces, a novel extension of classical algebraic topology.

Findings

Defined digital homology and cohomology modules.

Established properties of digital Hopf spaces.

Explored digital Pontryagin algebras and coalgebras.

Abstract

In the current study, we explore digital homology and cohomology modules, and investigate their fundamental properties on pointed digital images. We also examine pointed digital Hopf spaces and base point preserving digital Hopf functions between the pointed digital Hopf spaces with suitable digital multiplications, and explore the digital primitive homology and cohomology classes, the digital Pontryagin algebras and coalgebras on the digital Hopf spaces as digital images.