On the topological characterization of near force-free magnetic fields, and the work of late-onset visually-impaired topologists

P. Robert  Kotiuga

doi:10.3934/dcdss.2016.9.215

Article Contents

2016, Volume 9, Issue 1: 215-234. Doi: 10.3934/dcdss.2016.9.215

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On the topological characterization of near force-free magnetic fields, and the work of late-onset visually-impaired topologists

P. Robert Kotiuga^1,

1.
Boston University, ECE Dept, 8 Saint Mary's Street, Boston, MA 02215

Received: September 2014

Revised: February 2015

Published: February 2016

Abstract / Introduction Related Papers Cited by

Abstract

The Giroux correspondence and the notion of a near force-free magnetic field are used to topologically characterize near force-free magnetic fields which describe a variety of physical processes, including plasma equilibrium. As a byproduct, the topological characterization of force-free magnetic fields associated with current-carrying links, as conjectured by Crager and Kotiuga, is shown to be necessary and conditions for sufficiency are given. Along the way a paradox is exposed: The seemingly unintuitive mathematical tools, often associated to higher dimensional topology, have their origins in three dimensional contexts but in the hands of late-onset visually impaired topologists. This paradox was previously exposed in the context of algorithms for the visualization of three-dimensional magnetic fields. For this reason, the paper concludes by developing connections between mathematics and cognitive science in this specific context.

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Mathematics Subject Classification: 37D55, 53D35, 58Z99, 78A25.

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