\(\tau\)-invariants for knots in rational homology spheres

DOI10.2140/AGT.2020.20.1601zbMATH Open1448.57016arXiv1611.09415OpenAlexW2557768830MaRDI QIDQ784240

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Publication date: 3 August 2020

Published in: (Search for Journal in Brave)

Abstract: Ozsv'ath and Szab'o used the knot filtration on $widehatCF(S^3)$ to define the $au$-invariant for knots in the 3-sphere. In this article, we generalize their construction and define a collection of $au$-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 $Y$..

Full work available at URL: https://arxiv.org/abs/1611.09415

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