Homology of ternary algebras yielding invariants of knots and knotted surfaces

Niebrzydowski, Maciej¹

¹Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk, Poland

Algebraic and Geometric Topology, Tome 20 (2020) no. 5, pp. 2337-2372

Résumé

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.

Détail

DOI : 10.2140/agt.2020.20.2337

Classification : 57M27, 55N35, 57Q45
Keywords: ternary quasigroup, homology, Reidemeister moves, Roseman moves, Yoshikawa moves, cocycle invariant, degenerate subcomplex, link on a surface, knotted surface

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