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Linear independence of rationally slice knots

Jennifer Hom, Sungkyung Kang, JungHwan Park and Matthew Stoffregen

Geometry & Topology 26 (2022) 3143–3172
Abstract

A knot in S3 is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot concordance group. In particular, our examples are all infinite order. All previously known examples of rationally slice knots were order two.

Keywords
rationally slice knot, linear independence, involutive knot Floer homology
Mathematical Subject Classification
Primary: 57K10, 57K18
References
Publication
Received: 7 December 2020
Revised: 28 July 2021
Accepted: 1 September 2021
Published: 23 January 2023
Proposed: András I Stipsicz
Seconded: Ciprian Manolescu, Cameron Gordon
Authors
Jennifer Hom
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Sungkyung Kang
Sungkyung Kang
Center For Geometry and Physics
Institute of Basic Science
Pohang
South Korea
JungHwan Park
Department of Mathematical Sciences
KAIST
Daejeon
South Korea
Matthew Stoffregen
Department of Mathematics
Michigan State University
East Lansing, MI
United States