Degenerations of ideal hyperbolic triangulations

2005/08/16 by Stephan Tillmann, Tillmann, Stephan
Mathematics · #57M25 #57N10 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0508295

openalex publication_date 2005/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain projective classes of transversely measured singular codimension-one foliations of M. This leads to a combinatorial and geometric variant of well-known constructions by Culler, Morgan and Shalen concerning the character variety of a 3-manifold.

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