Kyoto Journal of Mathematics

On the collapsing along deformations of hyperbolic cone 3 -manifolds

Alexandre Paiva Barreto

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This article focuses on deformations of hyperbolic cone structures under the assumption that the length of the singularity remains uniformly bounded during the deformation. Let M be a closed, orientable, and irreducible 3 -manifold, and let Σ be an embedded link in M . For a collapsing sequence of hyperbolic cone structures with topological type ( M , Σ ) and with uniformly bounded lengths of singularities, we prove that M is either Seifert fibered or a Sol manifold.

Article information

Kyoto J. Math., Volume 56, Number 3 (2016), 539-557.

Received: 10 October 2014
Revised: 16 July 2015
Accepted: 30 July 2015
First available in Project Euclid: 22 August 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds

hyperbolic cone manifolds collapsing sequences deformations of structures


Barreto, Alexandre Paiva. On the collapsing along deformations of hyperbolic cone $3$ -manifolds. Kyoto J. Math. 56 (2016), no. 3, 539--557. doi:10.1215/21562261-3600166.

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