On d-invariants and generalized Kanenobu knots

Abstract

We prove that for particular infinite families of L-spaces, arising as branched double covers, the d-invariants defined by Ozsváth and Szabó are arbitrarily large and small. As a consequence, we generalise a result by Greene and Watson by proving, for every odd number ∆ ≥ 5, the existence of infinitely many nonquasi-alternating homologically thin knots with determinant ∆ 2 , and a result by Hoffman and Walsh concerning the existence of hyperbolic weight 1 manifolds that are not surgery on a knot in S 3 . * m.marengon13@imperial.ac.uk

The Big Dehn Surgery Graph and the link of 𝑆³

“…Remark 4.7. In [23], Marengon extends the techniques given here to exhibit an infinite four parameter family of double branched covers of knots given by a Kaneobu like construction.…”