Truncated Heegaard Floer homology and knot concordance invariants

Truong, Linh

doi:10.2140/agt.2019.19.1881

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Truncated Heegaard Floer homology and knot concordance invariants

Linh Truong

Algebraic & Geometric Topology 19 (2019) 1881–1901

DOI: 10.2140/agt.2019.19.1881

Abstract

We construct a sequence of smooth concordance invariants $ν_{n} (K)$ 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 $ν_{n}$ can be arbitrarily large. We also prove that the sequence $ν_{n}$ contains more concordance information than $τ$ , $ν$ , $ν^{'}$ , $ν^{+}$ and $ν^{+^{'}}$ .

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Keywords

knot theory, concordance, Heegaard Floer homology

Mathematical Subject Classification 2010

Primary: 57M25, 57M27, 57R58

References

Publication

Received: 21 January 2018

Revised: 10 November 2018

Accepted: 18 December 2018

Published: 16 August 2019

Authors

Linh Truong
Department of Mathematics Columbia University New York, NY United States

Volume 19, issue 4 (2019)