L-space surgeries on satellites by algebraic links

Sarah Dean Rasmussen

Published 2017-03-20Version 1

We provide an explicit description of the region of rational L-space surgery slopes for a torus-link satellite of any L-space knot in $S^3$ (including the unknot), with a result that precisely extends Hedden's and Hom's analogous result for cables. More generally, we characterize the region of rational L-space surgery slopes for satellites by algebraic links and for iterated satellites by torus-links. We also address implications for conjectures of Boyer-Gordon-Watson and Juh\'asz for surgeries on torus-link satellites of knots in $S^3$.