L-spaces and knot traces
File(s)
Accepted version
Author(s)
Baldwin, John A
Sivek, Steven
Type
Journal Article
Abstract
There has been a great deal of interest in understanding which knots are characterized by which of their Dehn surgeries. We study a 4-dimensional version of this question: which knots are determined by which of their traces? We prove several results that are in stark contrast with what is known about characterizing surgeries, most notably that the 0-trace detects every L-space knot.
Our proof combines tools in Heegaard Floer homology with results about surface homeomorphisms and their dynamics. We also consider nonzero traces, proving for instance that each positive torus knot is determined by its n-trace for any n ≤ 0, whereas no non-positive integer is known to be a characterizing slope for any positive torus knot besides the right-handed trefoil.
Our proof combines tools in Heegaard Floer homology with results about surface homeomorphisms and their dynamics. We also consider nonzero traces, proving for instance that each positive torus knot is determined by its n-trace for any n ≤ 0, whereas no non-positive integer is known to be a characterizing slope for any positive torus knot besides the right-handed trefoil.
Date Issued
2025-01-01
Date Acceptance
2026-03-13
Citation
Journal of the European Mathematical Society (Print)
ISSN
1435-9855
Publisher
EMS Press
Journal / Book Title
Journal of the European Mathematical Society (Print)
Copyright Statement
Copyright © 2026 Copyright Owner. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Identifier
http://arxiv.org/abs/2501.00914v1
Subjects
math.GT
math.GT
Publication Status
Accepted