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More concordance homomorphisms from knot Floer homology

Irving Dai, Jennifer Hom, Matthew Stoffregen and Linh Truong

Geometry & Topology 25 (2021) 275–338

We define an infinite family of linearly independent, integer-valued smooth concordance homomorphisms. Our homomorphisms are explicitly computable and rely on local equivalence classes of knot Floer complexes over the ring 𝔽[U,V ](UV = 0). We compare our invariants to other concordance homomorphisms coming from knot Floer homology, and discuss applications to topologically slice knots, concordance genus and concordance unknotting number.

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concordance, knots, knot Floer homology
Mathematical Subject Classification 2010
Primary: 57M25, 57N70, 57R58
Received: 15 March 2019
Revised: 13 December 2019
Accepted: 12 January 2020
Published: 2 March 2021
Proposed: András I Stipsicz
Seconded: Ciprian Manolescu, Peter Ozsváth
Irving Dai
Department of Mathematics
Princeton University
Princeton, NJ
United States
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Jennifer Hom
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Matthew Stoffregen
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Linh Truong
Department of Mathematics
Columbia University
New York, NY
United States
School of Mathematics
Institute for Advanced Study
Princeton, NJ
United States