Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^2$-Betti numbers and non-unitarizable groups without free subgroups   We show that there exist non-unitarizable groups without non-abelian free
subgroups. Both torsion and torsion free examples are constructed. As a
by-product, we show that there exist finitely generated torsion groups with
non-vanishing first $L^2$-Betti numbers. We also relate the well-known problem
of whether every hyperbolic group is residually finite to an open question
about approximation of $L^2$-Betti numbers.

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The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: q-alg