Kyoto Journal of Mathematics

On the collapsing along deformations of hyperbolic cone 3 -manifolds

Alexandre Paiva Barreto

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1471872280

Digital Object Identifier
doi:10.1215/21562261-3600166

Mathematical Reviews number (MathSciNet)
MR3542774

Zentralblatt MATH identifier
1354.57024

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

Keywords
hyperbolic cone manifolds collapsing sequences deformations of structures

Citation

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. https://projecteuclid.org/euclid.kjm/1471872280


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References

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