Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Augmentation Rank of Satellites with Braid Pattern   Given a knot $K$ in $S^3$, a question raised by Cappell and Shaneson asks if
the meridional rank of $K$ equals the bridge number of $K$. Using augmentations
in knot contact homology we consider the persistence of equality between these
two invariants under satellite operations on $K$ with a braid pattern. In
particular, we answer the question in the affirmative for a large class of
iterated torus knots.

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The categories of this paper are: cs
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci