Abstract
We discuss a connection between two fields that appear to have little in common: plasma physics and mathematical knot theory. Plasma physicists are interested in studying helicity conservation in magnetic flux ropes and knot theorists commonly consider “Reidemeister moves,” transformations that preserve a property called “knottedness.” To study the tangling, twisting, and untwisting of magnetic flux ropes, it is helpful to know which topological transformations conserve helicity. Although the second and third types of Reidemeister moves applied to a magnetic flux rope clearly conserve the helicity of the flux rope, the first type of Reidemeister move appears to be in conflict with helicity conservation. We show that all three Reidemeister moves conserve helicity in magnetic flux ropes.
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