Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A singular Poincare lemma   We prove a Poincare lemma for a set of r smooth functions on a 2n-dimensional
smooth manifold satisfying a commutation relation determined by r singular
vector fields associated to a Cartan subalgebra of $\frak{sp}(2r,\mathbb R)$.
This result has a natural interpretation in terms of the cohomology associated
to the infinitesimal deformation of a completely integrable system.

30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas