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On $d$ $d$ -invariants and generalized Kanenobu knots

Marco Marengon

Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK

E-mail Address: m.marengon13@imperial.ac.uk

https://doi.org/10.1142/S0218216516500486Cited by:1 (Source: Crossref)

Abstract

We prove that for particular infinite families of $L$ $L$ -spaces, arising as branched double covers, the $d$ $d$ -invariants defined by Ozsváth and Szabó assume arbitrarily large positive and negative values. As a consequence, we generalize a result by Greene and Watson by proving, for every odd number $Δ \geq 5$ $Δ \geq 5$ , the existence of infinitely many non-quasi-alternating homologically thin knots with determinant $Δ^{2}$ $Δ^{2}$ , and a result by Hoffman and Walsh concerning the existence of hyperbolic weight $1$ $1$ manifolds, that are not surgery on a knot in $S^{3}$ $S^{3}$ .

Keywords:

AMSC: 57M25, 57M27, 57M05, 57M12, 57M50

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