Degenerations of ideal hyperbolic triangulations |
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Authors: | Stephan Tillmann |
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Affiliation: | 1. School of Mathematics and Physics, The University of Queensland, Brisbane, QLD, 4072, Australia
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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. |
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