Neighborhoods of transverse knots and destabilizations
Preprint 2025

In this note we show that transverse knots have unique standard neighborhoods and prove a structure theorem about non-loose Legendrian knots. 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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