Distinguishing Power of 4-Legendrian Permutation Racks
Geometric Topology
2026-03-02 v2 Quantum Algebra
Abstract
We study 4-Legendrian racks and their effectiveness at distinguishing Legendrian knots. We prove that permutation racks with 4-Legendrian rack structures cannot distinguish Legendrian knots that share the same knot type, Thurston-Bennequin number, and rotation number. However, they also recover these three classical invariants.
Keywords
Cite
@article{arxiv.2510.26619,
title = {Distinguishing Power of 4-Legendrian Permutation Racks},
author = {Luc Ta and Peyton Phinehas Wood},
journal= {arXiv preprint arXiv:2510.26619},
year = {2026}
}
Comments
14 pages, 4 figures, 1 table