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A problem of Ulam about magnetic fields generated by knotted wires

Published online by Cambridge University Press:  27 November 2017

ALBERTO ENCISO  and
DANIEL PERALTA-SALAS
ALBERTO ENCISO
Affiliation:
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain email aenciso@icmat.es, dperalta@icmat.es
DANIEL PERALTA-SALAS
Affiliation:
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain email aenciso@icmat.es, dperalta@icmat.es
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Abstract

In the context of magnetic fields generated by wires, we study the connection between the topology of the wire and the topology of the magnetic lines. We show that a generic knotted wire has a magnetic line of the same knot type, but that given any pair of knots there is a wire isotopic to the first knot having a magnetic line isotopic to the second. These questions can be traced back to Ulam in 1935.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 8 , August 2019 , pp. 2048 - 2070
Copyright
© Cambridge University Press, 2017 

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