Some Properties of Higher Dimensional Homotopy Groups for Digital Images

Authors

Tane Vergili, Departments of Mathematics, Ege University Bornova Izmir, 35100 TurkeyFollow
Ismet Karaca, Departments of Mathematics, Ege University Bornova Izmir, 35100 TurkeyFollow

Author Country (or Countries)

Turkey

Abstract

By combining the algebraic topological concepts such as Euler characteristics, (co)homology groups, fundamental and homotopy groups with digital topology we can compare, classify or identify the digital images between each other. In this paper, we explore the digital relative homotopy relation between two continuous functions on a pointed digital image whose domains are n-cube and which map the boundary of an n-cube to a fix point. Then we introduce the nth homotopy group of a pointed digital image and give a relation between the homotopy groups of two pointed digital images.

Recommended Citation

Vergili, Tane and Karaca, Ismet (2015) "Some Properties of Higher Dimensional Homotopy Groups for Digital Images," Applied Mathematics & Information Sciences: Vol. 09: Iss. 6, Article 32.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss6/32