Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of hyperbolic 3-manifolds of a given volume   The work of Jorgensen and Thurston shows that there is a finite number N(v)
of orientable hyperbolic 3-manifolds with any given volume v. We show that
there is an infinite sequence of closed orientable hyperbolic 3-manifolds,
obtained by Dehn filling on the figure eight knot complement, that are uniquely
determined by their volumes. This gives a sequence of distinct volumes x_i
converging to the volume of the figure eight knot complement with N(x_i) = 1
for each i. We also give an infinite sequence of 1-cusped hyperbolic
3-manifolds, obtained by Dehn filling one cusp of the (-2,3,8)-pretzel link
complement, that are uniquely determined by their volumes amongst orientable
cusped hyperbolic 3-manifolds. Finally, we describe examples showing that the
number of hyperbolic link complements with a given volume v can grow at least
exponentially fast with v.

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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph