  In this paper we examine the relationship between various types of positivity
for knots and the concodance invariant tau discovered by Ozsvath and Szabo and
independently by Rasmussen. The main result shows that, for fibered knots, tau
characterizes strong quasipositivity. This is quantified by the statement that
for K fibered, tau(K)=g(K) if and only if K is strongly quasipositive. In
addition, we survey existing results regarding tau and forms of positivity and
highlight several consequences concerning the types of knots which are
(strongly) (quasi) positive. For instance, we show that any knot known to admit
a lens space surgery is strongly quasipositive and exhibit infinite families of
knots which are not quasipositive.
