Framed instanton homology and concordance
File(s)
Accepted version
Author(s)
Baldwin, John A
Sivek, Steven
Type
Journal Article
Abstract
We define two concordance invariants of knots using framed instanton homology. These invariants 𝜈♯ and 𝜏♯ provide bounds on slice genus and maximum self-linking number, and the latter is a concordance homomorphism which agrees in all known cases with the 𝜏 invariant in Heegaard Floer homology. We use 𝜈♯ and 𝜏♯ to compute the framed instanton homology of all nonzero rational Dehn surgeries on: 20 of the 35 nontrivial prime knots through eight crossings, infinite families of twist and pretzel knots, and instanton L-space knots; and of 19 of the first 20 closed hyperbolic manifolds in the Hodgson–Weeks census. In another application, we determine when the cable of a knot is an instanton L-space knot. Finally, we discuss applications to the spectral sequence from odd Khovanov homology to the framed instanton homology of branched double covers, and to the behaviors of 𝜏♯ and 𝜏 under genus-2 mutation.
Date Issued
2021-12-01
Date Acceptance
2021-09-14
Citation
Journal of Topology, 2021, 14 (4), pp.1113-1175
ISSN
1753-8416
Publisher
Wiley
Start Page
1113
End Page
1175
Journal / Book Title
Journal of Topology
Volume
14
Issue
4
Copyright Statement
© 2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
Identifier
https://arxiv.org/abs/2004.08699
Subjects
math.GT
math.GT
General Mathematics
0101 Pure Mathematics
Publication Status
Published
Date Publish Online
2021-10-12