Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero sets of Abelian Lie algebras of vector fields   Assume M is a 3-dimensional real manifold without boundary, A is an abelian
Lie algebra of analytic vector fields on M, and X is an element of A. The
following result is proved:
  If K is a locally maximal compact set of zeroes of X and the Poincar'e-Hopf
index of X at K is nonzero, there is a point in K at which all the elements of
A vanish.

19
The categories of this paper are: eess
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat