Volume 20, issue 5 (2020)

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Homology of ternary algebras yielding invariants of knots and knotted surfaces

Maciej Niebrzydowski

Algebraic & Geometric Topology 20 (2020) 2337–2372
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