Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
A uniformizable spherical CR structure on a two-cusped hyperbolic $3$–manifold

Yueping Jiang, Jieyan Wang and Baohua Xie

Algebraic & Geometric Topology 23 (2023) 4143–4184
Bibliography
1 M Acosta, Spherical CR Dehn surgeries, Pacific J. Math. 284 (2016) 257 MR3544300
2 M Acosta, Spherical CR uniformization of Dehn surgeries of the Whitehead link complement, Geom. Topol. 23 (2019) 2593 MR4019899
3 A F Beardon, The geometry of discrete groups, 91, Springer (1983) MR698777
4 M Culler, N M Dunfield, M Goerner, J R Weeks, SnapPy, a computer program for studying the geometry and topology of 3–manifolds, (2016)
5 M Deraux, On spherical CR uniformization of 3–manifolds, Exp. Math. 24 (2015) 355 MR3359222
6 M Deraux, A 1–parameter family of spherical CR uniformizations of the figure eight knot complement, Geom. Topol. 20 (2016) 3571 MR3590357
7 M Deraux, E Falbel, Complex hyperbolic geometry of the figure-eight knot, Geom. Topol. 19 (2015) 237 MR3318751
8 M Deraux, J R Parker, J Paupert, New non-arithmetic complex hyperbolic lattices, Invent. Math. 203 (2016) 681 MR3461365
9 E Falbel, A spherical CR structure on the complement of the figure eight knot with discrete holonomy, J. Differential Geom. 79 (2008) 69 MR2401419
10 E Falbel, P V Koseleff, F Rouillier, Representations of fundamental groups of 3–manifolds into PGL(3, ) : exact computations in low complexity, Geom. Dedicata 177 (2015) 229 MR3370032
11 E Falbel, J Wang, Branched spherical CR structures on the complement of the figure-eight knot, Michigan Math. J. 63 (2014) 635 MR3255694
12 W M Goldman, Complex hyperbolic geometry, Clarendon (1999) MR1695450
13 W M Goldman, J R Parker, Complex hyperbolic ideal triangle groups, J. Reine Angew. Math. 425 (1992) 71 MR1151314
14 W M Goldman, J R Parker, Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space, J. Geom. Anal. 2 (1992) 517 MR1189043
15 J Hempel, 3–Manifolds, 86, Princeton Univ. Press (1976) MR415619
16 J Ma, B Xie, Spherical CR uniformization of the magic 3–manifold, preprint (2021) arXiv:2106.06668
17 J Ma, B Xie, Menger curve and spherical CR uniformization of a closed hyperbolic 3–orbifold, preprint (2022) arXiv:2201.04765
18 J Ma, B Xie, Three-manifolds at infinity of complex hyperbolic orbifolds, preprint (2022) arXiv:2205.11167
19 G D Mostow, On a remarkable class of polyhedra in complex hyperbolic space, Pacific J. Math. 86 (1980) 171 MR586876
20 J R Parker, Notes on complex hyperbolic geometry, (2003)
21 J R Parker, J Wang, B Xie, Complex hyperbolic (3,3,n) triangle groups, Pacific J. Math. 280 (2016) 433 MR3453571
22 J R Parker, P Will, A complex hyperbolic Riley slice, Geom. Topol. 21 (2017) 3391 MR3692969
23 R E Schwartz, Degenerating the complex hyperbolic ideal triangle groups, Acta Math. 186 (2001) 105 MR1828374
24 R E Schwartz, Ideal triangle groups, dented tori, and numerical analysis, Ann. of Math. 153 (2001) 533 MR1836282
25 R E Schwartz, Complex hyperbolic triangle groups, from: "Proceedings of the International Congress of Mathematicians, II" (editor T Li), Higher Ed. (2002) 339 MR1957045
26 R E Schwartz, Real hyperbolic on the outside, complex hyperbolic on the inside, Invent. Math. 151 (2003) 221 MR1953259
27 R E Schwartz, A better proof of the Goldman–Parker conjecture, Geom. Topol. 9 (2005) 1539 MR2175152
28 R E Schwartz, Spherical CR geometry and Dehn surgery, 165, Princeton Univ. Press (2007) MR2286868
29 J O Wyss-Gallifent, Complex hyperbolic triangle groups, PhD thesis, University of Maryland (2000) MR2700554