Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Virtual Bridge Number One Knots   We define the virtual bridge number $vb(K)$ and the virtual unknotting number
$vu(K)$ invariants for virtual knots. For ordinary knots $K$ they are closely
related to the bridge number $b(K)$ and the unknotting number $u(K)$ and we
have $vu(K)\leq u(K), vb(K)\leq b(K).$
  There are no ordinary knots $K$ with $b(K)=1.$ We show there are infinitely
many homotopy classes of virtual knots each of which contains infinitely many
isotopy classes of $K$ with $vb(K)=1.$ In fact for each $i\in \N$ there exists
$K$ virtually homotopic (but not virtually isotopic) to the unknot with
$vb(K)=1$ and $vu(K)=i.$

28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio