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- Title
Degenerations of ideal hyperbolic triangulations.
- Authors
Tillmann, Stephan
- Abstract
Let M be a cusped 3-manifold, and let $${\mathcal{T}}$$ be an ideal triangulation of M. The deformation variety $${\mathfrak{D}(\mathcal{T})}$$ , a subset of which parameterises (incomplete) hyperbolic structures obtained on M using $${\mathcal{T}}$$ , 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.
- Subjects
MANIFOLDS (Mathematics); DIFFERENTIAL geometry; GEOMETRIC topology; TRIANGULATION; MATHEMATICS
- Publication
Mathematische Zeitschrift, 2012, Vol 272, Issue 3/4, p793
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-011-0958-8