$\tau$-invariants for knots in rational homology spheres

Abstract

Ozsváth and Szabó 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 $Y$..

34 pages, 10 figures

References in corpus (3)

• Floer homology and knot complements
• On concordances in 3-manifolds
• A refinement of the Ozsváth-Szabó large integer surgery formula and knot concordance

Cited by in corpus (5)

• On contact type hypersurfaces in 4-space
• Null surgery on knots in L-spaces
• Upsilon invariants from cyclic branched covers
• Contact (+1)-surgeries on rational homology 3-spheres
• A bound for rational Thurston-Bennequin invariants