Knot Floer homology and the unknotting number

Akram Alishahi; Eaman Eftekhary

doi:10.2140/gt.2020.24.2435

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arXiv · 1810.05125

Knot Floer homology and the unknotting number

Akram Alishahi·Eaman Eftekhary

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Abstract

Given a knot K in S^3, 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 is greater than or equal to the \nu^-(K). Moreover, the difference l(K)-\nu^-(K) can be arbitrarily large. We also present several applications towards bounding the unknotting number, the alteration number and the Gordian distance.

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BibTeX RIS

Akram Alishahi, Eaman Eftekhary. 2018-10-11. Knot Floer homology and the unknotting number. https://doi.org/10.2140/gt.2020.24.2435

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