Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some hyperbolic 4-manifolds with low volume and number of cusps   We construct here two new examples of non-orientable, non-compact, hyperbolic
4-manifolds. The first has minimal volume $v_m = 4{\pi}^2/3$ and two cusps.
This example has the lowest number of cusps among known minimal volume
hyperbolic 4-manifolds. The second has volume $2\cdot v_m$ and one cusp. It has
lowest volume among known one-cusped hyperbolic 4-manifolds.

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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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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: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th