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2020 Knot Floer homology and the unknotting number
Akram Alishahi, Eaman Eftekhary
Geom. Topol. 24(5): 2435-2469 (2020). DOI: 10.2140/gt.2020.24.2435

Abstract

Given a knot KS3, let u(K) (respectively, u+(K)) denote the minimum number of negative (respectively, positive) crossing changes among all unknotting sequences for K. We use knot Floer homology to construct the invariants 𝔩(K), 𝔩+(K) and 𝔩(K), which give lower bounds on u(K), u+(K) and the unknotting number u(K), respectively. The invariant 𝔩(K) only vanishes for the unknot, and satisfies 𝔩(K)ν+(K), while the difference 𝔩(K)ν+(K) can be arbitrarily large. We also present several applications towards bounding the unknotting number, the alteration number and the Gordian distance.

Citation

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Akram Alishahi. Eaman Eftekhary. "Knot Floer homology and the unknotting number." Geom. Topol. 24 (5) 2435 - 2469, 2020. https://doi.org/10.2140/gt.2020.24.2435

Information

Received: 10 November 2018; Revised: 19 December 2019; Accepted: 10 March 2020; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194296
Digital Object Identifier: 10.2140/gt.2020.24.2435

Subjects:
Primary: 57M27

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.24 • No. 5 • 2020
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