Online, hosted by the ICMS Edinburgh, 7 May 2020
Baptiste Chantraine. Invariants of Legendrian submanifolds in non-coorientable contact structures.
I want to report on some work in progress about understanding Legendrian submanifolds in contact manifolds where the contact structure is not coorientable (in the talk I will focus mainly on the space of contact element of an euclidian space). We will see two structures arising when considering the Z_2 action on the lift of the Legendrian to its coorientation cover: one is a structure of involution on the augmentation category and the other is a Z_2 equivariant version of linearised Legendrian contact homology. At the end of the talk I will relate the latter to other equivariant theories which could be used to compute it in some natural situations arising from the conormal construction. I will begin by introducing the objects involved and will recall what are the classical version of these invariants.
András Juhász. Transverse invariants and exotic surfaces in the 4-ball.
We explain how use 1-twist rim surgery to construct infinitely many smoothly embedded, orientable surfaces in the 4-ball bounding a knot in the 3-sphere that are pairwise topologically isotopic, but not ambient diffeomorphic. We distinguish the surfaces using the maps they induce on perturbed knot Floer homology, together with our result that the cobordism map induced by an ascending surface in a Weinstein cobordism preserves the transverse invariant in knot Floer homology. This is joint work with Maggie Miller and Ian Zemke.