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$L$–space knots have no essential Conway spheres

Tye Lidman, Allison H Moore and Claudius Zibrowius

Geometry & Topology 26 (2022) 2065–2102
Abstract

We prove that L–space knots do not have essential Conway spheres with the technology of peculiar modules, a Floer-theoretic invariant for tangles.

Keywords
$L$–space knots, Conway spheres
Mathematical Subject Classification
Primary: 57K18
Secondary: 57K30, 57R58
References
Publication
Received: 15 June 2020
Revised: 2 March 2021
Accepted: 19 June 2021
Published: 12 December 2022
Proposed: András I Stipsicz
Seconded: Peter Ozsváth, Ciprian Manolescu
Authors
Tye Lidman
Department of Mathematics
North Carolina State University
Raleigh, NC
United States
https://sites.google.com/ncsu.edu/tlid/home
Allison H Moore
Department of Mathematics and Applied Mathematics
Virginia Commonwealth University
Richmond, VA
United States
https://people.vcu.edu/~moorea14/
Claudius Zibrowius
Fakultät für Mathematik
Universität Regensburg
Regensburg
Germany
https://cbz20.raspberryip.com/