Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fully Augmented Links in the Thickened Torus   In this paper we study the geometry of fully augmented link complements in
the thickened torus and describe their geometric properties, generalizing the
study of fully augmented links in $S^3$. We classify which fully augmented
links in the thickened torus are hyperbolic, show that their complements in the
thickened torus decompose into ideal right-angled torihedra, and that the edges
of this decomposition are canonical. We also study volume density of fully
augmented links in $S^3$, defined to be the ratio of its volume and the number
of augmentations. We prove the Volume Density Conjecture for fully augmented
links which states that the volume density of a sequence of fully augmented
links in $S^3$ which diagrammatically converge to a biperiodic link, converges
to the volume density of that biperiodic link.

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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci