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arXiv · 1810.12943

H-principle for complex contact structures on Stein manifolds

Franc Forstneric
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Abstract

In this paper we introduce the notion of a formal complex contact structure on an odd dimensional complex manifold. Our main result is that every formal complex contact structure on a Stein manifold $X$ is homotopic to a holomorphic contact structure on a Stein domain $\Omega\subset X$ which is diffeotopic to $X$. We also prove a parametric h-principle in this setting, analogous to Gromov's h-principle for contact structures on smooth open manifolds. On Stein threefolds we obtain a complete homotopy classification of formal complex contact structures. Our methods also furnish a parametric h-principle for germs of holomorphic contact structures along totally real submanifolds of class $\mathscr C^2$ in arbitrary complex manifolds.

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Franc Forstneric. 2018-10-30. H-principle for complex contact structures on Stein manifolds. https://doi.org/10.4310/jsg.2020.v18.n3.a4

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