Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A problem of Ulam about magnetic fields generated by knotted wires   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.

0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an