Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functions on surfaces and incompressible subsurfaces   Let $M$ be a smooth connected compact surface and $P$ be either a real line
or a circle. This paper proceeds the study of the stabilizers and orbits of
smooth functions on $M$ with respect to the right action of the group of
diffeomorphisms of $M$. A large class of smooth maps $f:M\to P$ with isolated
singularities is considered and it is shown that the general problem of
calculation of the fundamental group of the orbit of $f$ reduces to the case
when the Euler characteristic of $M$ is non-negative. For the proof of main
result incompressible subsurfaces and cellular automorphisms of surfaces are
investigated.

0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org