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Degenerations of ideal hyperbolic triangulations

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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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  1. School of Mathematics and Physics, The University of Queensland, Brisbane, QLD, 4072, Australia

    Stephan Tillmann

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Tillmann, S. Degenerations of ideal hyperbolic triangulations. Math. Z. 272, 793–823 (2012). https://doi.org/10.1007/s00209-011-0958-8

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