Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An analytic invariant of G_2 manifolds   We prove that the moduli space of holonomy G_2-metrics on a closed 7-manifold
is in general disconnected by presenting a number of explicit examples.
  We detect different connected components of the G_2-moduli space by defining
an integer-valued analytic refinement of the nu-invariant, a Z/48-valued defect
invariant of G_2-structures on a closed 7-manifold introduced by the first and
third authors. The refined invariant is defined using eta invariants and
Mathai-Quillen currents on the 7-manifold and we compute it for twisted
connected sums \`a la Kovalev, Corti-Haskins-Nordstr\"om-Pacini and
extra-twisted connected sums as constructed by the second and third authors. In
particular, we find examples of G_2-holonomy metrics in different components of
the moduli space where the associated G_2-structures are homotopic and other
examples where they are not.

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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol