Combinatorial invariants of transverse links via cyclic branched covers

Triangle Topology Seminar

Mike Wong (Louisiana State University)

Tuesday, January 23, 2018 -
4:30pm to 5:30pm

Grid homology is a version of knot Floer homology in the 3-sphere that is entirely combinatorial and simple to define. Exploiting this, Ozsvath, Szabo, and Thurston defined a combinatorial invariant of transverse links in the 3-sphere using grid homology, which was then used to show that certain knot types are transversely non-simple by Ng, Ozsvath, and Thurston. This is particularly interesting because there are few invariants well suited for such purpose. More generally, there is also an invariant for transverse links in an arbitrary 3-manifold defined by Lisca, Ozsvath, Stipsicz, and Szabo, using an open-book decomposition. However, this invariant is difficult to compute in general. In this talk, for a transverse link in the 3-sphere, we will define combinatorial invariants by considering its lifts in its cyclic branched covers, using Levine's grid-like diagrams for knot Floer homology, and show that they coincide with the LOSS invariants for the lifts. This is joint work with Shea Vela-Vick.

Last updated: 2018/01/20 - 4:21am