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Noded Teichmueller spaces

Ruben H. Hidalgo·Alexnader Vasil'ev
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Abstract

Let $G$ be a finitely generated Kleinian group and let $Δ$ be an invariant collection of components in its region of discontinuity. The Teichmüller space $T(Δ,G)$ supported in $Δ$, is the space of equivalence classes of quasiconformal homeomorphisms with complex dilatation invariant under $G$ and supported in $Δ$. In this paper we propose a partial closure of $T(Δ,G)$ by considering certain deformations of the above homeomorphisms. Such a partial closure is denoted by $NT(Δ,G)$ and called the {\it noded Teichmüller space} of $G$ supported in $Δ$. Some concrete examples are discussed.

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Ruben H. Hidalgo, Alexnader Vasil'ev. 2005-09-16. Noded Teichmueller spaces. https://arxiv.org/abs/math/0509381

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