τ-invariants for knots in rational homology spheres

τ-invariants for knots in rational homology spheres

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Katherine Raoux, Michigan State University/Bryn Mawr
Fine Hall 314

Using the knot filtration on the Heegaard Floer chain complex, Ozsváth and Szabó defined an invariant of knots in the three sphere called τ(K) and showed that it is a lower bound for the 4-ball genus. Generalizing their construction, I will show that for a (not necessarily null-homologous) knot, K, in a rational homology sphere, Y, we obtain a collection of τ-invariants, one for each spin-c structure on Y.  In addition, 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.