Straightening cell decompositions of cusped hyperbolic 3-manifolds

Pescini, Marina

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 2, pp. 101-109

Résumé

Let \( M \) be an oriented cusped hyperbolic 3-manifold and let \( \tau \) be a topological ideal triangulation of \( M \). We give a characterization for \( \tau \) to be isotopic to an ideal geodesic triangulation; moreover we give a characterization for \( \tau \) to flatten into a partially flat triangulation. Finally we prove that straightening combinatorially equivalent topological ideal cell decompositions gives the same geodesic decomposition, up to isometry.