Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing theorems for associative submanifolds   Let M^7 a manifold with holonomy in G_2, and Y^3 an associative submanifold
with boundary in a coassociative submanifold. In [5], the authors proved that
M_{X,Y}, the moduli space of its associative deformations with boundary in the
fixed X, has finite virtual dimension. Using Bochner's technique, we give a
vanishing theorem that forces M_{X,Y} to be locally smooth.

20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ