Geometry & Topology Volume 19, issue 1 (2015)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Complex hyperbolic geometry of the figure-eight knot

Martin Deraux and Elisha Falbel

Geometry & Topology 19 (2015) 237–293

DOI: 10.2140/gt.2015.19.237

Bibliography

1	A F Beardon, The geometry of discrete groups, 91, Springer (1995) MR1393195
2	N Bergeron, E Falbel, A Guilloux, Tetrahedra of flags, volume and homology of SL(3), Geom. Topol. 18 (2014) 1911 MR3268771
3	D Burns Jr., S Shnider, Spherical hypersurfaces in complex manifolds, Invent. Math. 33 (1976) 223 MR0419857
4	M Deraux, Deforming the ℝ–Fuchsian (4,4,4)–triangle group into a lattice, Topology 45 (2006) 989 MR2263221
5	E Falbel, A spherical CR–structure on the complement of the figure eight knot with discrete holonomy, J. Differential Geom. 79 (2008) 69 MR2401419
6	E Falbel, P V Koseleff, F Rouiller, Representations of fundamental groups of 3–manifolds into PGL(3, ℂ) : Exact computations in low complexity, to appear in Geom. Dedicata
7	E Falbel, J Wang, Branched sperical CR–structures on the complement of the figure-eight knot, Michigan Math. J. 63 (2014) 635 MR3255694
8	S Garoufalidis, M Goerner, C K Zickert, Gluing equations for PGL(n, ℂ)–representations of 3–manifolds, arXiv:1207.6711
9	W M Goldman, Conformally flat manifolds with nilpotent holonomy and the uniformization problem for 3–manifolds, Trans. Amer. Math. Soc. 278 (1983) 573 MR701512
10	W M Goldman, Complex hyperbolic geometry, Clarendon Press (1999) MR1695450
11	B Maskit, Kleinian groups, 287, Springer (1988) MR959135
12	G D Mostow, On a remarkable class of polyhedra in complex hyperbolic space, Pacific J. Math. 86 (1980) 171 MR586876
13	J R Parker, Complex hyperbolic Kleinian groups, in preparation
14	M B Phillips, Dirichlet polyhedra for cyclic groups in complex hyperbolic space, Proc. Amer. Math. Soc. 115 (1992) 221 MR1107276
15	R Riley, A quadratic parabolic group, Math. Proc. Cambridge Philos. Soc. 77 (1975) 281 MR0412416
16	D Rolfsen, Knots and links, 7, Publish or Perish (1990) MR1277811
17	R E Schwartz, Degenerating the complex hyperbolic ideal triangle groups, Acta Math. 186 (2001) 105 MR1828374
18	R E Schwartz, Real hyperbolic on the outside, complex hyperbolic on the inside, Invent. Math. 151 (2003) 221 MR1953259
19	R E Schwartz, Spherical CR–geometry and Dehn surgery, 165, Princeton Univ. Press (2007) MR2286868
20	W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)