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

Volume 25, 1 issue

Volume 24, 9 issues

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
Presentations for cusped arithmetic hyperbolic lattices

Alice Mark and Julien Paupert

Algebraic & Geometric Topology 22 (2022) 3577–3626
Bibliography
1 D Allcock, New complex- and quaternion-hyperbolic reflection groups, Duke Math. J. 103 (2000) 303 MR1760630
2 M Belolipetsky, On volumes of arithmetic quotients of SO(1,n), Ann. Sc. Norm. Super. Pisa Cl. Sci. 3 (2004) 749 MR2124587
3 L Bianchi, Sui gruppi di sostituzioni lineari con coefficienti appartenenti a corpi quadratici immaginarî, Math. Ann. 40 (1892) 332 MR1510727
4 W Bosma, J Cannon, C Playoust, The Magma algebra system, I : The user language, J. Symbolic Comput. 24 (1997) 235
5 D I Cartwright, T Steger, Enumeration of the 50 fake projective planes, C. R. Math. Acad. Sci. Paris 348 (2010) 11 MR2586735
6 D I Cartwright, T Steger, Finding generators and relations for groups acting on the hyperbolic ball, preprint (2017) arXiv:1701.02452
7 S S Chen, L Greenberg, Hyperbolic spaces, from: "Contributions to analysis : a collection of papers dedicated to Lipman Bers" (editors L V Ahlfors, I Kra, B Maskit, L Nirenberg), Academic (1974) 49 MR0377765
8 J H Conway, D A Smith, On quaternions and octonions: their geometry, arithmetic, and symmetry, A K Peters (2003) MR1957212
9 J P Díaz, A Verjovsky, F Vlacci, Quaternionic Kleinian modular groups and arithmetic hyperbolic orbifolds over the quaternions, Geom. Dedicata 192 (2018) 127 MR3749425
10 E Falbel, G Francsics, J R Parker, The geometry of the Gauss–Picard modular group, Math. Ann. 349 (2011) 459 MR2753829
11 E Falbel, J R Parker, The geometry of the Eisenstein–Picard modular group, Duke Math. J. 131 (2006) 249 MR2219242
12 I Kim, J R Parker, Geometry of quaternionic hyperbolic manifolds, Math. Proc. Cambridge Philos. Soc. 135 (2003) 291 MR2006066
13 A M Macbeath, Groups of homeomorphisms of a simply connected space, Ann. of Math. 79 (1964) 473 MR160848
14 A Mark, Lattice presentations, companion files and notebooks to this paper (2021)
15 J Paupert, P Will, Real reflections, commutators, and cross-ratios in complex hyperbolic space, Groups Geom. Dyn. 11 (2017) 311 MR3641843
16 Z Phillippe, Invariants globaux des espaces hyperboliques quaternioniques, PhD thesis, Université de Bordeaux (2016)
17 D Polletta, Presentations for the Euclidean Picard modular groups, Geom. Dedicata 210 (2021) 1 MR4200907
18 G Prasad, Volumes of S–arithmetic quotients of semi-simple groups, Inst. Hautes Études Sci. Publ. Math. 69 (1989) 91 MR1019962
19 C L Siegel, Discontinuous groups, Ann. of Math. 44 (1943) 674 MR9959
20 R Steinberg, Some consequences of the elementary relations in SLn, from: "Finite groups: coming of age", Contemp. Math. 45, Amer. Math. Soc. (1985) 335 MR822247
21 M Stover, Volumes of Picard modular surfaces, Proc. Amer. Math. Soc. 139 (2011) 3045 MR2811261
22 R G Swan, Generators and relations for certain special linear groups, Advances in Math. 6 (1971) 1 MR284516
23 J M Woodward, Integral lattices and hyperbolic manifolds, PhD thesis, The University of York (2006) MR2715950
24 D Yasaki, Integral cohomology of certain Picard modular surfaces, J. Number Theory 134 (2014) 13 MR3111555
25 T Zhao, Generators for the Euclidean Picard modular groups, Trans. Amer. Math. Soc. 364 (2012) 3241 MR2888244
26 T Zink, Über die Anzahl der Spitzen einiger arithmetischer Untergruppen unitärer Gruppen, Math. Nachr. 89 (1979) 315 MR546890