Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative Property (T) and the Vanishing of the first $\ell^2$-Betti
  number   In this paper, we show that certain families with relative property (T) have
trivial first $\ell^2$-Betti number. We apply this to the elementary matrix
group $\EL_n(\R)$ where $\R$ is any countable unital ring of characteristic 0.

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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
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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: acc-phys
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex