- 4607B South Hall
Copy-Paste methods in contact topology
A Legendrian knot is a knot whose tangents lie in the contact planes of a contact structure. Legendrian knots have a very simple form in the standard contact structure. Namely Legendrian knots can be entirely recovered from their projection by lifting every point to the height that equals the slope in the projection. Legendrian isotopy is an isotopy through only Legendrian knots. Legendrian isotopy classes refine smooth isotopy classes in an interesting way. Several invariants has been introduced to distinguish Legendrian knots. After a short introduction to Legendrian knots and their invariants I will talk about how one can try to use copy-paste methods to classify Legendrian knots in some smooth knot types. This is a joint work with John Etnyre.