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Cone 3-Manifolds

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In the Tradition of Thurston II

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Abstract

This is an overview on hyperbolic cone 3-manifolds, their deformation theory and their role in Thurston’s orbifold theorem. We also describe the phenomena that may occur when deforming the cone angles, like cusp opening or collapses, under the assumption that the cone angles are less than π.

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Acknowledgements

I thank Ken’ichi Ohshika and Athanase Papadopoulos for the oportunity of writing this survey and for their suggestions that improved it. I acknowledge support by the FEDER/AEI/MICIU grant PGC2018-095998-B-I00 “Local and global invariants in geometry”.

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Authors and Affiliations

  1. Departament de Matemàtiques UAB and Centre de Recerca Matemàtica, Cerdanyola del Vallès, Spain

    Joan Porti

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  1. Joan Porti
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Correspondence to Joan Porti .

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Editors and Affiliations

  1. Department of Mathematics, Gakushuin University, Tokyo, Japan

    Ken’ichi Ohshika

  2. Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS, Strasbourg, France

    Athanase Papadopoulos

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Porti, J. (2022). Cone 3-Manifolds. In: Ohshika, K., Papadopoulos, A. (eds) In the Tradition of Thurston II. Springer, Cham. https://doi.org/10.1007/978-3-030-97560-9_4

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