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Truncated Heegaard Floer homology and knot concordance invariants

Linh Truong

Algebraic & Geometric Topology 19 (2019) 1881–1901

We construct a sequence of smooth concordance invariants νn(K) defined using truncated Heegaard Floer homology. The invariants generalize the concordance invariants ν of Ozsváth and Szabó and ν+ of Hom and Wu. We exhibit an example in which the gap between two consecutive elements in the sequence νn can be arbitrarily large. We also prove that the sequence νn contains more concordance information than τ, ν, ν, ν+ and ν+ .

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knot theory, concordance, Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57R58
Received: 21 January 2018
Revised: 10 November 2018
Accepted: 18 December 2018
Published: 16 August 2019
Linh Truong
Department of Mathematics
Columbia University
New York, NY
United States