Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal unknotting sequences of Reidemeister moves containing unmatched
  RII moves   Arnold introduced invariants $J^+$, $J^-$ and $St$ for generic planar curves.
  It is known that both $J^+ /2 + St$ and $J^- /2 + St$ are invariants for
generic spherical curves.
  Applying these invariants to underlying curves of knot diagrams, we can
obtain lower bounds for the number of Reidemeister moves for uknotting.
  $J^- /2 + St$ works well for unmatched RII moves.
  However, it works only by halves for RI moves.
  Let $w$ denote the writhe for a knot diagram.
  We show that $J^- /2 + St \pm w/2$ works well also for RI moves, and
demonstrate that it gives a precise estimation for a certain knot diagram of
the unknot with the underlying curve $r = 2 + \cos (n \theta/(n+1)),\ (0 \le
\theta \le 2(n+1)\pi$).

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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph