Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformation theory of nearly $\mathrm{G}_2$ manifolds   We study the deformation theory of nearly $\mathrm{G}_2$ manifolds. These are
seven dimensional manifolds admitting real Killing spinors. We show that the
infinitesimal deformations of nearly $\mathrm{G}_2$ structures are obstructed
in general. Explicitly, we prove that the infinitesimal deformations of the
homogeneous nearly $\mathrm{G}_2$ structure on the Aloff--Wallach space are all
obstructed to second order. We also completely describe the cohomology of
nearly $\mathrm{G}_2$ manifolds.

30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th