Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linking number of vortices as baryon number   We show that the topological degree of a Skyrmion field is the same as the
Hopf charge of the field under the Hopf map and thus equals the linking number
of the preimages of two points on the 2-sphere under the Hopf map. We further
interpret two particular points on the 2-sphere as vortex zeros and the linking
of these zero lines follows from the latter theorem. Finally we conjecture that
the topological degree of the Skyrmion can be interpreted as the product of
winding numbers of vortices corresponding to the zero lines, summing over
clusters of vortices.

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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci