Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: G3-homogeneous gravitational instantons   We provide an exhaustive classification of self-dual four-dimensional
gravitational instantons foliated with three-dimensional homogeneous spaces,
i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces
admitting a Bianchi simply transitive isometry group. The classification
pattern is based on the algebra homomorphisms relating the Bianchi group and
the duality group SO(3). New and general solutions are found for Bianchi III.

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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: math
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph