Journal of Differential Geometry

A spherical CR structure on the complement of the figure eight knot with discrete holonomy

E. Falbel

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Abstract

We describe a general geometrical construction of representations of fundamental groups of 3-manifolds into PU(2, 1) and eventually of spherical CR structures defined on those 3-manifolds. We construct branched spherical CR structures on the complement of the figure eight knot and the Whitehead link. They have discrete holonomies contained in PU(2, 1,Z[ω]) and PU(2, 1,Z[i]) respectively.

Article information

Source
J. Differential Geom., Volume 79, Number 1 (2008), 69-110.

Dates
First available in Project Euclid: 10 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1207834658

Digital Object Identifier
doi:10.4310/jdg/1207834658

Mathematical Reviews number (MathSciNet)
MR2401419

Zentralblatt MATH identifier
1148.57025

Citation

Falbel, E. A spherical CR structure on the complement of the figure eight knot with discrete holonomy. J. Differential Geom. 79 (2008), no. 1, 69--110. doi:10.4310/jdg/1207834658. https://projecteuclid.org/euclid.jdg/1207834658


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