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arXiv · 2510.26619

Distinguishing Power of 4-Legendrian Permutation Racks

Luc Ta·Peyton Phinehas Wood
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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.

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Luc Ta, Peyton Phinehas Wood. 2025-10-30. Distinguishing Power of 4-Legendrian Permutation Racks. https://arxiv.org/abs/2510.26619

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