## Topology Seminar (Main Talk): The transverse invariant and braid dynamics

Seminar | November 14 | 4:10-5 p.m. | 3 Evans Hall

Lev Tovstopyat-Nelip, Boston College

Department of Mathematics

Let $K$ be a link braided about an open book $(B,p)$ supporting a contact manifold $(Y,\xi )$. $K$ and $B$ are naturally transverse links. We prove that the hat version of the transverse link invariant defined by Baldwin, Vela-Vick and Vertesi is non-zero for the union of $K$ with $B$. As an application, we prove that the transverse invariant of any braid having fractional Dehn twist coefficient greater than one is non-zero. We discuss geometric consequences and future directions.

conway@berkeley.edu