Neighborhoods of transverse knots and destabilizations

John B. Etnyre

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arXiv · 2512.15651

Neighborhoods of transverse knots and destabilizations

John B. Etnyre

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Abstract

In this note, we show that transverse knots have unique standard neighborhoods and prove a structure theorem about non-loose Legendrian knots. We also prove a finiteness result for transverse knots in a tight contact manifold. The common theme of these two results is a general destabilization result for Legendrian knots. As a byproduct of this work, we find a manifold with an infinite number of distinct tight contact structures, up to contactomoprhism, with no Giroux torsion.

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John B. Etnyre. 2025-12-17. Neighborhoods of transverse knots and destabilizations. https://arxiv.org/abs/2512.15651

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