| Ozsvath and Szabo used the knot filtration on the Heegaard-Floer chain complex of the 3-sphere to define the tau-invariant. In this thesis, we generalize their construction and define a collection of tau-invariants, one for each spinc-structure, associated to a rationally null-homologous knot K in a rational homology sphere Y. We also show that these invariants can be used to obtain a lower bound on the genus of a surface with boundary K properly embedded in a negative definite 4-manifold with boundary Y.. |
