Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Topology of Foliations with a First Integral   The main objective of this article is to study the topology of the fibers of
a generic rational function of the type $F^p/G^q$ in the projective space of
dimension two. We will prove that the action of the monodromy group on a single
Lefschetz vanishing cycle $\delta$ generates the first homology group of a
generic fiber of $F^p/G^q$. In particular, we will prove that for any two
Lefschetz vanishing cycles $\delta_0$ and $\delta_1$ in a regular compact fiber
of $F^p/G^q$, there exists a monodromy $h$ such that $h(\delta_0)=\pm
\delta_1$.

35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex