Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete non-compact Spin(7) manifolds from self-dual Einstein
  4-orbifolds   We present an analytic construction of complete non-compact 8-dimensional
Ricci-flat manifolds with holonomy Spin(7). The construction relies on the
study of the adiabatic limit of metrics with holonomy Spin(7) on principal
Seifert circle bundles over asymptotically conical G2 orbifolds. The metrics we
produce have an asymptotic geometry, so-called ALC geometry, that generalises
to higher dimensions the geometry of 4-dimensional ALF hyperk\"ahler metrics.
We apply our construction to asymptotically conical G2 metrics arising from
self-dual Einstein 4-orbifolds with positive scalar curvature. As illustrative
examples of the power of our construction, we produce complete non-compact
Spin(7) manifolds with arbitrarily large second Betti number and infinitely
many distinct families of ALC Spin(7) metrics on the same smooth 8-manifold.

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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an