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

TL;DR

This paper demonstrates that the collapse page of the Lee spectral sequence bounds the unknotting number and confirms the Knight Move Conjecture for knots with unknotting number less than 3.

Contribution

It establishes a link between the spectral sequence collapse page and unknotting number, proving the Knight Move Conjecture for knots with u(K)<3.

Findings

Spectral sequence collapse bounds unknotting number

Knots with u(K)<3 have spectral sequence collapsing at E_2

Knight Move Conjecture holds for knots with u(K)<3

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.