Hyperbolic L-space knots not concordant to algebraic knots

Maciej Borodzik and Masakazu Teragaito

Vol. 335 (2025), No. 1, 33–51

DOI: 10.2140/pjm.2025.335.33

Abstract

We construct infinitely many hyperbolic L-space knots for which $-3\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->\mathrm{{\rm Y}}$ is not an integer, where $\mathrm{{\rm Y}}$ is the Ozsváth–Stipsicz–Szabó upsilon function. None of these knots can be concordant to a linear combination of algebraic knots.

Keywords

L-space knot, hyperbolic knot, upsilon function

Mathematical Subject Classification

Primary: 57K18

Milestones

Received: 28 May 2024

Revised: 20 January 2025

Accepted: 27 January 2025

Published: 24 March 2025