On a homology of ternary groups with applications to knot theory

TL;DR

This paper introduces a homology theory for ternary groups, explores their construction via odd-even methods, and applies these concepts to define ternary knot groups and analyze their homomorphisms, advancing knot theory research.

Contribution

It presents a new homology framework for ternary groups, introduces the odd-even construction for generating examples, and applies these to ternary knot groups in knot theory.

Findings

Established a homology theory for ternary groups

Developed the odd-even construction for ternary groups

Applied ternary groups to knot theory through ternary knot groups

Abstract

We define a homology for ternary groups using both associativity and skew elements. We describe the odd-even construction which yields many examples of ternary groups. We define the ternary knot group, consider its homomorphisms into ternary groups, and discuss the applications.