Noded Teichmueller spaces

Details Noded Teichmueller spaces Noded Teichmueller spaces

2005-09-16

arxiv.org/abs/math/0509381v1

J. Anal. Math. 99 (2006), 89-107

Mathematics

Complex Variables

18 pages, 1 figure

Scientific paper

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

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