David Shea Vela-Vick, Univ. of Pennsylvania

TITLE: Transverse invariants and bindings of open books

ABSTRACT: Let T be a transverse knot in (Y, xi) which is the binding of some open book, (T, pi), for the ambient contact manifold (Y, xi). In this talk, we show that the transverse invariant, defined by Lisca, Ozsváth, Stipsicz, and Szabó (LOSS), is nonvanishing for such transverse knots. We will also discuss a vanishing theorem for the invariants defined by LOSS. As a corollary, we will see that if (T, pi) is an open book with connected binding, then the complement of T has no Giroux torsion.  Time permitting, we will also talk about a generalization of this theorem which removes the connected binding condition.