Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Satellites of Infinite Rank in the Smooth Concordance Group   We conjecture that satellite operations are either constant or have infinite
rank in the concordance group. We reduce this to the difficult case of winding
number zero satellites, and use $SO(3)$ gauge theory to provide a general
criterion sufficient for the image of a satellite operation to generate an
infinite rank subgroup of the smooth concordance group $\mathcal{C}$. Our
criterion applies widely; notably to many unknotted patterns for which the
corresponding operators on the topological concordance group are zero. We raise
some questions and conjectures regarding satellite operators and their
interaction with concordance.

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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: econ