Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Virtual Homotopy   Two welded (respectively virtual) link diagrams are homotopic if one may be
transformed into the other by a sequence of extended Reidemeister moves,
classical Reidemeister moves, and self crossing changes. In this paper, we
extend Milnor's mu and bar mu invariants to welded and virtual links. We
conclude this paper with several examples, and compute the mu invariants using
the Magnus expansion and Polyak's skein relation for the mu invariants.

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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: q-bio