Algebraic & Geometric Topology Volume 20, issue 2 (2020)

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): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

A new nonarithmetic lattice in ${\rm PU}(3,1)$

Martin Deraux

Algebraic & Geometric Topology 20 (2020) 925–963

DOI: 10.2140/agt.2020.20.925

Bibliography

1	E Bannai, Fundamental groups of the spaces of regular orbits of the finite unitary reflection groups of dimension 2, J. Math. Soc. Japan 28 (1976) 447 MR407199
2	G Barthel, F Hirzebruch, T Höfer, Geradenkonfigurationen und Algebraische Flächen, D4, Vieweg (1987) MR912097
3	M V Belolipetsky, S A Thomson, Systoles of hyperbolic manifolds, Algebr. Geom. Topol. 11 (2011) 1455 MR2821431
4	D Bessis, Finite complex reflection arrangements are K(π,1), Ann. of Math. 181 (2015) 809 MR3296817
5	D Bessis, J Michel, Explicit presentations for exceptional braid groups, Experiment. Math. 13 (2004) 257 MR2103323
6	M Broué, G Malle, R Rouquier, Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math. 500 (1998) 127 MR1637497
7	K Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. 135 (1992) 165 MR1147961
8	W Couwenberg, G Heckman, E Looijenga, Geometric structures on the complement of a projective arrangement, Publ. Math. Inst. Hautes Études Sci. 101 (2005) 69 MR2217047
9	H S M Coxeter, Regular complex polytopes, Cambridge Univ. Press (1991) MR1119304
10	P Deligne, G D Mostow, Monodromy of hypergeometric functions and nonlattice integral monodromy, Inst. Hautes Études Sci. Publ. Math. 63 (1986) 5 MR849651
11	P Deligne, G D Mostow, Commensurabilities among lattices in PU(1,n), 132, Princeton Univ. Press (1993) MR1241644
12	M Deraux, Non-arithmetic ball quotients from a configuration of elliptic curves in an abelian surface, Comment. Math. Helv. 93 (2018) 533 MR3854901
13	M Deraux, Non-arithmetic lattices and the Klein quartic, J. Reine Angew. Math. 754 (2019) 253 MR4000575
14	M Deraux, Volumes of 3–ball quotients as intersection numbers, Trans. Amer. Math. Soc. 373 (2020) 343 MR4042878
15	M Deraux, J R Parker, J Paupert, New non-arithmetic complex hyperbolic lattices, Invent. Math. 203 (2016) 681 MR3461365
16	M Deraux, J R Parker, J Paupert, New non-arithmetic complex hyperbolic lattices, II, preprint (2016) arXiv:1611.00330
17	H Esnault, M Groechenig, Rigid connections and F–isocrystals, preprint (2017) arXiv:1707.00752
18	W M Goldman, Complex hyperbolic geometry, Oxford Univ. Press (1999) MR1695450
19	M Gromov, I Piatetski-Shapiro, Nonarithmetic groups in Lobachevsky spaces, Inst. Hautes Études Sci. Publ. Math. 66 (1988) 93 MR932135
20	M Gromov, R Schoen, Harmonic maps into singular spaces and p–adic superrigidity for lattices in groups of rank one, Inst. Hautes Études Sci. Publ. Math. 76 (1992) 165 MR1215595
21	R P Holzapfel, Chern numbers of algebraic surfaces : Hirzebruch’s examples are Picard modular surfaces, Math. Nachr. 126 (1986) 255 MR846579
22	R P Holzapfel, Ball and surface arithmetics, E29, Vieweg (1998) MR1685419
23	G A Margulis, Discrete groups of motions of manifolds of nonpositive curvature, from: "Proceedings of the International Congress of Mathematicians" (editor R D James), Canadian Mathematical Congress (1975) 21 MR0492072
24	G D Mostow, On a remarkable class of polyhedra in complex hyperbolic space, Pacific J. Math. 86 (1980) 171 MR586876
25	M S Raghunathan, Discrete subgroups of Lie groups, 68, Springer (1972) MR0507234
26	G C Shephard, J A Todd, Finite unitary reflection groups, Canad. J. Math. 6 (1954) 274 MR59914
27	T Terada, Problème de Riemann et fonctions automorphes provenant des fonctions hypergéométriques de plusieurs variables, J. Math. Kyoto Univ. 13 (1973) 557 MR481156
28	S Thomson, Quasi-arithmeticity of lattices in PO(n,1), Geom. Dedicata 180 (2016) 85 MR3451458
29	W P Thurston, Shapes of polyhedra and triangulations of the sphere, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1, Geom. Topol. Publ. (1998) 511 MR1668340