Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing $\nu$-invariants of Joyce's compact $G_2$-manifolds   Crowley and Nordstr\"{o}m introduced an invariant of $G_2$-structures on the
tangent bundle of a closed 7-manifold, taking values in the integers modulo 48.
Using the spectral description of this invariant due to Crowley, Goette and
Nordstr\"{o}m, we compute it for many of the closed torsion-free
$G_2$-manifolds defined by Joyce's generalized Kummer construction.

28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci