Unknotting with a single twist
Samantha Allen, Charles Livingston
TL;DR
This paper investigates the conditions under which a knot can be unknotted with a single twist, developing obstructions using advanced knot invariants and Heegaard Floer theory.
Contribution
It introduces new obstructions to unknotting knots with a single twist based on classical invariants, Casson-Gordon invariants, and Heegaard Floer theory.
Findings
Identifies conditions preventing unknotting with one twist
Uses classical invariants and advanced theories for obstructions
Provides a framework for analyzing twist-based unknotting
Abstract
Given a knot in the three-sphere, is it possible to unknot it by performing a single twist, and if so, what are the possible linking numbers of such a twist? We develop obstructions to unknotting using a twist of a specified linking number. The obstructions we describe are built using classical knot invariants, Casson-Gordon invariants, and Heegaard Floer theory.
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