Noded Teichmueller spaces

Abstract

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.