Characterizing slopes for Legendrian knots

Abstract: Characterizing slopes for Legendrian knots: From a given Legendrian knot K in the standard contact 3-sphere, we can construct a symplectic 4-manifold W_K by attaching a Weinstein 2-handle along K to the 4-ball. In this talk, we will construct non-equivalent Legendrian knots K and K' such that W_K and W_K' are equivalent. On the other hand, we will discuss an example of a Legendrian knot K that is characterized by its symplectic 4-manifold W_K. This is based on joint work with Roger Casals and John Etnyre. No previous knowledge on contact geometry is assumed. We will discuss all relevant notions in detail.

algebraic topologydifferential geometrygeometric topologyK-theory and homology

Audience: researchers in the topic

Göttingen topology and geometry seminar

Series comments: Our seminar takes place via zoom every Tuesday afternoon (Central European Summer Time; the precise time slot varies—please always refer to the listing).