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

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arxiv 1611.09415 v2 pith:MYEGL7UM submitted 2016-11-28 math.GT

Katherine Raoux This is my paper · ORCID
classification math.GT
keywords invariantsboundarydefinehomologyknotknotsrationalsphere
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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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Cited by 1 Pith paper

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  1. Exotic Mazur manifolds and knot trace invariants

    math.GT 2019-08 conditional novelty 8.0 of 10

    Exotic Mazur manifolds exist, and the knot Floer invariant ν is shown to be an invariant of knot traces, yielding counterexamples to a conjecture in Kirby's problem list.

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