The Lee Spectral Sequence, Unknotting Number, and the Knight Move Conjecture

Akram Alishahi; Nathan Dowlin

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arXiv · 1710.07875

The Lee Spectral Sequence, Unknotting Number, and the Knight Move Conjecture

Akram Alishahi·Nathan Dowlin

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Abstract

We show that the page at which the Lee spectral sequence collapses gives a bound on the unknotting number, u(K). In particular, for knots with u(K)<3, we show that the Lee spectral sequence must collapse at the E_2 page. An immediate corollary is that the Knight Move Conjecture is true when u(K)<3.

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Akram Alishahi, Nathan Dowlin. 2017-10-22. The Lee Spectral Sequence, Unknotting Number, and the Knight Move Conjecture. https://arxiv.org/abs/1710.07875

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