no. 7
Geometry
Constructing spherical CR manifolds by gluing tetrahedra
[Structures CR sphériques par recollement de tétrahèdres]

Présenté par : Étienne Ghys

Falbel, Elisha1
1 Institut de mathématiques, analyse algébrique, 175, rue du Chevaleret, 75005 Paris, France
Comptes Rendus. Mathématique, Tome 340 (2005) no. 7, pp. 503-506.

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).

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).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.02.014
Falbel, Elisha 1

1 Institut de mathématiques, analyse algébrique, 175, rue du Chevaleret, 75005 Paris, France 
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Falbel, Elisha. Constructing spherical CR manifolds by gluing tetrahedra. Comptes Rendus. Mathématique, Tome 340 (2005) no. 7, pp. 503-506. doi : 10.1016/j.crma.2005.02.014. http://www.numdam.org/articles/10.1016/j.crma.2005.02.014/

[1] Falbel, E.; Zocca, V. A Poincaré's polyhedron theorem for complex hyperbolic geometry, J. Reine Angew. Math., Volume 516 (1999), pp. 133-158

[2] Goldman, W.M. Complex Hyperbolic Geometry, Oxford Math. Monographs, Oxford University Press, 1999

[3] Riley, R. A quadratic parabolic group, Math. Proc. Cambridge Philos. Soc., Volume 77 (1975), pp. 281-288

[4] Schwartz, R. Real hyperbolic on the outside, complex hyperbolic on the inside, Invent. Math., Volume 151 (2003) no. 2, pp. 221-295

[5] Schwartz, R. Spherical CR Geometry and Dehn Surgery Research Monograph, 2004

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

[7] Will, P. 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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