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Homology of ternary
algebras yielding invariants of knots and knotted
surfaces
Maciej Niebrzydowski |
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Algebraic & Geometric Topology 20 (2020) 2337–2372
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Abstract |
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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. |
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Keywords
ternary quasigroup, homology, Reidemeister moves, Roseman
moves, Yoshikawa moves, cocycle invariant, degenerate
subcomplex, link on a surface, knotted surface
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 55N35, 57Q45
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References |
Publication
Received: 19 July 2017
Revised: 5 June 2019
Accepted: 3 October 2019
Published: 4 November 2020
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Authors |
| Maciej Niebrzydowski | |
| Institute of Mathematics Faculty of Mathematics, Physics and Informatics University of Gdańsk Gdańsk Poland |
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