The Thurston boundary of Teichmuller space and complex of curves

Abstract

Let $S$ be a closed orientable surface with genus $g\ge 2$. For a sequence $\s_i$ in the Teichmüller space of $S$, which converges to a projective measured lamination $[\lam]$ in the Thurston boundary, we obtain a relation between $\lam$ and the geometric limit of pants decompositions whose lengths are uniformly bounded by a Bers constant $L$. We also show that this bounded pants decomposition is related to the Gromov boundary of complex of curves.

30 pages, 12 figures

References in corpus (3)

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
• Minimal stretch maps between hyperbolic surfaces
• Kleinian groups and the complex of curves