Homology of ternary algebras yielding 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.