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- Title
C^0-limits of Legendrian knots.
- Authors
Rizell, Georgios Dimitroglou; Sullivan, Michael G.
- 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 contactomorphic to the original knot. We prove this by establishing that, on one hand, non–Legendrian knots admit a type of contact-squashing (similar to squeezing) onto transverse knots while, on the other hand, Legendrian knots do not admit such a squashing. The non-trivial input from contact topology that is needed is (a local version of) the Thurston–Bennequin inequality.
- Subjects
KNOT theory; SQUASHES; TOPOLOGY
- Publication
Transactions of the American Mathematical Society, Series B, 2024, Vol 11, p798
- ISSN
2330-0000
- Publication type
Article
- DOI
10.1090/btran/189