Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Morse functions on the 2-sphere   This paper was motivated by work of Arnold where he explains how to count
"snakes", i.e. Morse functions on the real axis with prescribed behavior at
infinity. This leads immediately to a count of excellent Morse functions on the
circle, where following Thom's terminology, excellent means that no two
critical points lie on the same level set.
  We explain how to count equivalence classes of excellent Morse functions on
the 2-sphere. We consider two equivalence relations. The geometric relation
(two functions are equivalent if one can be obtained from the other via
compositions with an orientation preserving diffeomorphism of the sphere and an
orientation preserving diffeomorphism of the real axis) and the homology
relation (two functions are equivalent if the Betti numbers of the sublevel
sets undergo similar changes when crossing a critical value).

19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin