# Homology of ternary algebras yielding invariants of knots and knotted surfaces

## TL;DR

This paper develops a homology theory for ternary algebras based on axioms linked to particle scattering and Reidemeister moves, providing new invariants for knots and knotted surfaces.

## Contribution

It introduces a novel homology framework for ternary algebras that produces invariants of knots and knotted surfaces, connecting algebraic structures with topological invariants.

## Key findings

- Homology of ternary algebras derived from particle scattering axioms.
- Ternary quasigroups naturally relate to knot invariants.
- Normalized homology yields invariants of knots and knotted surfaces.

## Abstract

We define homology of ternary algebras satisfying axioms derived from particle scattering or, equivalently, from the third Reidemeister move. We show that ternary quasigroups satisfying these axioms appear naturally in invariants of Reidemeister, Yoshikawa, and Roseman moves. Our homology has a degenerate subcomplex. The normalized homology yields invariants of knots and knotted surfaces.