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On the topological characterization of near force-free magnetic fields, and the work of late-onset visually-impaired topologists. (English) Zbl 1336.53094

Summary: 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 J. C. Crager and the author [“Cuts for the magnetic scalar potential in knotted geometries and force-free magnetic fields”, IEEE Trans. Magn. 38, No. 2, 1309–1312 (2002; doi:10.1109/TMAG.2002.996334)], 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.

MSC:

53D35 Global theory of symplectic and contact manifolds
78A25 Electromagnetic theory (general)
00A66 Mathematics and visual arts
01A50 History of mathematics in the 18th century
01A55 History of mathematics in the 19th century
00A30 Philosophy of mathematics
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References:

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