Meagerness of the set of compact leaves for transversely holomorphic foliations
Bruno Scardua
TL;DR
This paper establishes a precise criterion linking the existence of a stable compact leaf in a transversely holomorphic foliation to the non-meagerness of the set of all compact leaves on a compact complex manifold.
Contribution
It provides a characterization of stable compact leaves via the topological property of the set of compact leaves being non-meager.
Findings
A stable compact leaf exists if and only if the set of compact leaves is non-meager.
The set of compact leaves is meager if no stable compact leaf exists.
The result connects foliation stability with Baire category concepts.
Abstract
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a meager subset of the manifold.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometry and complex manifolds · Advanced Differential Equations and Dynamical Systems