Ozsváth and Szabó used the knot filtration on to define the –invariant for knots in the –sphere. We generalize their construction and define a collection of –invariants associated to a knot in a rational homology sphere . We then show that some of these invariants provide lower bounds for the genus of a surface with boundary properly embedded in a negative-definite –manifold with boundary .
"$\tau$–invariants for knots in rational homology spheres." Algebr. Geom. Topol. 20 (4) 1601 - 1640, 2020. https://doi.org/10.2140/agt.2020.20.1601