  Ozsv\'ath and Szab\'o used the knot filtration on $\widehat{CF}(S^3)$ to
define the $\tau$-invariant for knots in the 3-sphere. In this article, we
generalize their construction and define a collection of $\tau$-invariants
associated to a knot $K$ in a rational homology sphere $Y$. We then show that
some of these invariants provide lower bounds for the genus of a surface with
boundary $K$ properly embedded in a negative definite 4-manifold with boundary
$Y$..
