Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: G2 geometry and integrable systems   We study the Hitchin component in the space of representations of the
fundamental group of a Riemann surface into a split real simple Lie group in
the rank 2 case. We prove that such representations are described by a
conformal structure and class of Higgs bundle we call cyclic and we show cyclic
Higgs bundles correspond to a form of the affine Toda equations. In each case
we relate cyclic Higgs bundles to geometric structures on the surface. We
elucidate the geometry of generic 2-plane distributions in 5 dimensions,
relating it to a parabolic geometry associated to the split real form of $G_2$
and a conformal geometry with holonomy in $G_2$. We prove the distribution is
the bundle of maximal isotropics corresponding to the annihilator of a spinor
satisfying the twistor-spinor equation. We study the moduli space of
coassociative submanifolds of a $G_2$-manifold with an aim towards
understanding coassociative fibrations. We consider coassociative fibrations
where the fibres are orbits of a $T^4$-action of isomorphisms and prove a local
equivalence to minimal 3-manifolds in $R^{3,3}\cong H^2(T^4,\mathbb{R})$ with
positive induced metric.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th