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

Banff International Research Station for Mathematical Innovation and Discovery

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), which they also showed 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. 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.

Mathematics; Manifolds and cell complexes; Global analysis, analysis on manifolds; Low dimensional topology

video/mp4

Author affiliation: Brandeis

2018-02-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64566

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/