On the Topology of Foliations with a First Integral

Hossein Movasati

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On the Topology of Foliations with a First Integral

Hossein Movasati

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Abstract

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 $δ$ 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 $δ_0$ and $δ_1$ in a regular compact fiber of $F^p/G^q$, there exists a monodromy $h$ such that $h(δ_0)=\pm δ_1$.

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BibTeX RIS

Hossein Movasati. 2002-06-07. On the Topology of Foliations with a First Integral. https://arxiv.org/abs/math/0206075

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