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

Katherine Raoux

doi:10.2140/agt.2020.20.1601

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arXiv · 1611.09415

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

Katherine Raoux

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Abstract

Ozsv\'ath and Szab\'o 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 $Y$..

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Katherine Raoux. 2016-11-28. $\tau$-invariants for knots in rational homology spheres. https://doi.org/10.2140/agt.2020.20.1601

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