Report
$C^0$-limits of Legendrian knots and contact non-squeezing
| العنوان: | $C^0$-limits of Legendrian knots and contact non-squeezing |
|---|---|
| المؤلفون: | Rizell, Georgios Dimitroglou, Sullivan, Michael G. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Symplectic Geometry, 53D10 |
| الوصف: | 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. Comment: 24 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2201.04579 |
| رقم الانضمام: | edsarx.2201.04579 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |