τ–invariants for knots in rational homologyspheres

Abstract

Ozsváth and Szabó used the knot filtration on [math] to define the [math] –invariant for knots in the [math] –sphere. We generalize their construction and define a collection of [math] –invariants associated to a knot [math] in a rational homology sphere [math] . We then show that some of these invariants provide lower bounds for the genus of a surface with boundary [math] properly embedded in a negative-definite [math] –manifold with boundary [math] .