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.