Homology of ternary algebras yielding invariants of knots and knotted surfaces

Niebrzydowski, Maciej

doi:10.2140/agt.2020.20.2337

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Homology of ternary algebras yielding invariants of knots and knotted surfaces

Maciej Niebrzydowski

Algebraic & Geometric Topology 20 (2020) 2337–2372

DOI: 10.2140/agt.2020.20.2337

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.

Keywords

ternary quasigroup, homology, Reidemeister moves, Roseman moves, Yoshikawa moves, cocycle invariant, degenerate subcomplex, link on a surface, knotted surface

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 55N35, 57Q45

References

Publication

Received: 19 July 2017

Revised: 5 June 2019

Accepted: 3 October 2019

Published: 4 November 2020

Authors

Maciej Niebrzydowski
Institute of Mathematics Faculty of Mathematics, Physics and Informatics University of Gdańsk Gdańsk Poland

Volume 20, issue 5 (2020)