Comptes Rendus
no. 7
Geometry
Constructing spherical CR manifolds by gluing tetrahedra

Presented by: Étienne Ghys

Elisha Falbel1
1 Institut de mathématiques, analyse algébrique, 175, rue du Chevaleret, 75005 Paris, France
Comptes Rendus. Mathématique, Volume 340 (2005) no. 7, pp. 503-506.

We propose a general method of constructing spherical CR manifolds by gluing tetrahedra adapted to CR geometry. We obtain spherical CR structures on the complement of the figure eight knot and the Whitehead link complement with holonomy in PU(2,1,Z[ω]) and PU(2,1,Z[i]) respectively (the same integer rings appearing in real hyperbolic geometry).

On propose une méthode de construction géométrique des variétés CR sphériques par recollement des tétrahèdres. Pour les complémentaires de la figure huit et l'entrelac de Whitehead, on obtient des structures avec holonomies dans PU(2,1,Z[ω]) et PU(2,1,Z[i]) respectivement (les mêmes anneaux d'entiers que dans le cas hyperbolique réel).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.02.014

Elisha Falbel 1

1 Institut de mathématiques, analyse algébrique, 175, rue du Chevaleret, 75005 Paris, France 
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Elisha Falbel. Constructing spherical CR manifolds by gluing tetrahedra. Comptes Rendus. Mathématique, Volume 340 (2005) no. 7, pp. 503-506. doi : 10.1016/j.crma.2005.02.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.02.014/

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[6] W. Thurston, The geometry and topology of 3-manifolds, Lecture notes, 1979

[7] P. Will Lagrangian decomposability of some two-generator subgroups of PU(2,1), C. R. Acad. Sci. Paris, Ser. I, Volume 340 (2005) no. 5, pp. 353-358

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