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In the context of magnetic fields generated by wires, we study the connectionbetween the topology of the wire and the topology of the magnetic lines. Weshow that a generic knotted wire has a magnetic line of the same knot type, butthat given any pair of knots there is a wire isotopic to the first knot havinga magnetic line isotopic to the second. These questions can be traced back toUlam in 1935.

A problem of Ulam about magnetic fields generated by knotted wires