## Kyoto Journal of Mathematics

### On the collapsing along deformations of hyperbolic cone $3$-manifolds

Alexandre Paiva Barreto

#### 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 $\Sigma$ be an embedded link in $M$. For a collapsing sequence of hyperbolic cone structures with topological type $(M,\Sigma )$ and with uniformly bounded lengths of singularities, we prove that $M$ is either Seifert fibered or a $\mathrm{Sol}$ manifold.

#### Article information

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

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

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

#### 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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