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arXiv · 1703.04666

Real Structures on Marked Schottky Space

Ruben A. Hidalgo·Sebastian Sarmiento
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Abstract

Schottky groups are exactly those Kleinian groups providing the regular lowest planar uniformizations of closed Riemann surfaces and also the ones providing to the interior of a handlebody of a complete hyperbolic structure with injectivity radius bounded away from zero. The space parametrizing quasiconformal deformations of Schottky groups of a fixed rank $g \geq 1$ is the marked Schottky space ${\mathcal M}{\mathcal S}_{g}$; this being a complex manifold of dimension $3(g-1)$ for $g \geq 2$ and being isomorphic to the punctured unit disc for $g=1$. In this paper we provide a complete description of the real structures of ${\mathcal M}{\mathcal S}_{g}$, up to holomorphic automorphisms, together their real part.

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Ruben A. Hidalgo, Sebastian Sarmiento. 2017-03-14. Real Structures on Marked Schottky Space. https://doi.org/10.1112/jlms.12131

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