Abstract
We study topological conditions that must be satisfied by a compactC ∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ∞ boundary such that Ω ≅ ℂ2.
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