Constructing spherical CR manifolds by gluing tetrahedra

Abstract

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). To cite this article: E. Falbel, C. R. Acad. Sci. Paris, Ser. I 340 (2005).