$C^0$-limits of Legendrian knots and contact non-squeezing

Georgios Dimitroglou Rizell; Michael G. Sullivan

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arXiv · 2201.04579

$C^0$-limits of Legendrian knots and contact non-squeezing

Georgios Dimitroglou Rizell·Michael G. Sullivan

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Abstract

Take a sequence of contactomorphisms of a contact three-manifold that $C^0$-converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this sequence, we show that it is Legendrian. We prove this by establishing that, on one hand, non-Legendrian knots admit a type of contact-squeezing onto transverse knots while, on the other, Legendrian knots do not admit such a squeezing. The non-trivial input from contact topology that is needed is (a local version of) the Thurston--Bennequin inequality.

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BibTeX RIS

Georgios Dimitroglou Rizell, Michael G. Sullivan. 2022-01-12. $C^0$-limits of Legendrian knots and contact non-squeezing. https://arxiv.org/abs/2201.04579

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