Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Limit Multiplicity for arithmetic hyperbolic surfaces and
  $3$-manifolds   We show that every sequence of torsion-free arithmetic congruence lattices in
$\mathrm{PGL}(2,\mathbb R)$ or $\mathrm{PGL}(2,\mathbb C)$ satisfies a strong
quantitative version of the Limit Multiplicity property. We deduce that for
$R>0$ in certain range, growing linearly in the degree of the invariant trace
field, the volume of the $R$-thin part of any congruence arithmetic hyperbolic
surface or congruence arithmetic hyperbolic $3$-manifold $M$ is of order at
most $\mathrm{Vol}(M)^{11/12}$. As an application we prove Gelander's
conjecture on homotopy type of arithmetic hyperbolic $3$-manifolds: We show
that there are constants $A,B$ such that every such manifold $M$ is homotopy
equivalent to a simplicial complex with at most $A\mathrm{Vol}(M)$ vertices,
all of degrees bounded by $B$.

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The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
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The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: stat