Geodesic
Hyperbolic cone-manifolds with large cone-angles
Souto, Juan1
1 Mathematisches Institut, Universität Bonn, Beringstr. 1, 53115 Bonn, Germany
Geometry & topology, Tome 7 (2003) no. 2, pp. 789-797.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We prove that every closed oriented 3–manifold admits a hyperbolic cone–manifold structure with cone–angle arbitrarily close to 2π.

DOI : 10.2140/gt.2003.7.789
Keywords: hyperbolic cone–manifold, Kleinian groups

Souto, Juan 1

1 Mathematisches Institut, Universität Bonn, Beringstr. 1, 53115 Bonn, Germany 
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Souto, Juan. Hyperbolic cone-manifolds with large cone-angles. Geometry & topology, Tome 7 (2003) no. 2, pp. 789-797. doi : 10.2140/gt.2003.7.789. http://geodesic.mathdoc.fr/articles/10.2140/gt.2003.7.789/

[1] M Boileau, J Porti, Geometrization of 3–orbifolds of cyclic type, Astérisque (2001) 208

[2] F Bonahon, J P Otal, Laminations measurées de plissage des variétés hyperboliques de dimension 3, Ann. of Math. $(2)$ 160 (2004) 1013

[3] K Bromberg, Rigidity of geometrically finite hyperbolic cone-manifolds, Geom. Dedicata 105 (2004) 143

[4] R D Canary, D B A Epstein, P Green, Notes on notes of Thurston, from: "Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984)", London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 3

[5] C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1

[6] K Matsuzaki, M Taniguchi, Hyperbolic manifolds and Kleinian groups, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press (1998)

[7] S P Kerckhoff, The measure of the limit set of the handlebody group, Topology 29 (1990) 27

[8] S Kojima, Deformations of hyperbolic 3–cone-manifolds, J. Differential Geom. 49 (1998) 469

[9] H Masur, Measured foliations and handlebodies, Ergodic Theory Dynam. Systems 6 (1986) 99

[10] J P Otal, Courants géodésiques et produits libres, Thèse d’Etat, Université Paris–Sud, Orsay (1988)

[11] J P Otal, Thurston's hyperbolization of Haken manifolds, from: "Surveys in differential geometry, Vol III (Cambridge, MA, 1996)", Int. Press, Boston (1998) 77

[12] J Souto, Geometric structures on 3–manifolds and their deformations, Bonner Mathematische Schriften 342, Universität Bonn Mathematisches Institut (2001)

[13] W P Thurston, The Geometry and Topology of 3–manifolds, lecture notes (1979)

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