Non-contractible loops of Legendrian tori from families of knots

2026/02/12 by Yukihiro Okamoto, Marián Poppr · 1 voice
Mathematics · #math.SG #math.GT

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Abstract

In the unit cotangent bundle of ℝ³, we consider loops of Legendrian tori arising as families of the unit conormal bundles of smooth knots in ℝ³. 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.

Discussions

• Yukihiro Okamoto, Mari\'an Poppr: Non-contractible loops of Legendrian tori from families of knots https://arxiv.org/abs/2602.11538 https://arxiv.org/pdf/2602.11538 https://arxiv.org/html/2602.11538 [bsky, 0 points, 0 comments]

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