  Consider a transverse knot which is the binding of an open book for the
ambient contact manifold. In this paper, we show that the transverse invariants
defined by Lisca, Ozsvath, Stipsicz, and Szabo (LOSS) are nonvanishing for such
transverse knots. This is true regardless of whether or not the ambient contact
structure is tight. We also prove a vanishing theorem for LOSS's Legendrian and
transverse invariants. As a corollary, we show that if (T,\pi) is an open book
with connected binding, then the complement of T has no Giroux torsion.
