C⁰-limits of Legendrian knots and contact non-squeezing

2022/01/12 by Rizell, Georgios Dimitroglou, Sullivan, Michael G. · 3 citations
#53D10 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2201.04579

Abstract

Take a sequence of contactomorphisms of a contact three-manifold that C⁰-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.

Cited by

• Legendrian barriers in prequantization bundles
• C⁰-rigidity of Legendrians and coisotropics via sheaf quantization
• C⁰-Contact Geometry of Surfaces in 3-Manifolds

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