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arXiv · 2602.11538

Non-contractible loops of Legendrian tori from families of knots

Yukihiro Okamoto·Marián Poppr
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Abstract

In the unit cotangent bundle of $\mathbb{R}^3$, we consider loops of Legendrian tori arising as families of the unit conormal bundles of smooth knots in $\mathbb{R}^3$. In this paper, using the cord algebra of knots, we give a topological method to compute the monodromy on the Legendrian contact homology in degree $0$ induced by those loops. As an application, we obtain an infinite family of non-contractible loops of Legendrian tori which are contractible in the space of smoothly embedded tori.

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Yukihiro Okamoto, Marián Poppr. 2026-02-12. Non-contractible loops of Legendrian tori from families of knots. https://arxiv.org/abs/2602.11538

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