Digital Hurewicz Theorem and Digital Homology Theory
Algebraic Topology
2020-05-19 v3
Abstract
In this paper, we develop homology groups for digital images based on cubical singular homology theory for topological spaces. Using this homology, we present digital Hurewicz theorem for the fundamental group of digital images. We also show that the homology functors developed in this paper satisfy properties that resemble the Eilenberg-Steenrod axioms of homology theory, in particular, the homotopy and the excision axioms. We finally define axioms of digital homology theory.
Keywords
Cite
@article{arxiv.1902.02274,
title = {Digital Hurewicz Theorem and Digital Homology Theory},
author = {Samira Sahar Jamil and Danish Ali},
journal= {arXiv preprint arXiv:1902.02274},
year = {2020}
}