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

Volume 26
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

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
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
Cusp-transitive $4$-manifolds with every cusp section

Jacopo Guoyi Chen and Edoardo Rizzi

Algebraic & Geometric Topology 26 (2026) 1077–1093
Bibliography
1 M Belolipetsky, T Gelander, A Lubotzky, A Shalev, Counting arithmetic lattices and surfaces, Ann. of Math. (2) 172 (2010) 2197 MR2726109
2 M Burger, T Gelander, A Lubotzky, S Mozes, Counting hyperbolic manifolds, Geom. Funct. Anal. 12 (2002) 1161 MR1952926
3 M Chein, Recherche des graphes des matrices de Coxeter hyperboliques d’ordre 10, Rev. Franaise Informat. Recherche Opérationnelle 3 (1969) 3 MR294181
4 J H Conway, J P Rossetti, Describing the platycosms, preprint (2003) arXiv:math/0311476
5 M W Davis, The geometry and topology of Coxeter groups, 32, Princeton Univ. Press (2008) MR2360474
6 M W Davis, Lectures on orbifolds and reflection groups, from: "Transformation groups and moduli spaces of curves" (editors L Ji, S T Yau), Adv. Lect. Math. (ALM) 16, International (2011) 63 MR2883685
7 A Felikson, P Tumarkin, Hyperbolic Coxeter polytopes,
8 L Ferrari, A Kolpakov, L Slavich, Cusps of hyperbolic 4-manifolds and rational homology spheres, Proc. Lond. Math. Soc. (3) 123 (2021) 636 MR4368684
9 R Guglielmetti, CoxIter, GitHub repository
10 R Guglielmetti, CoxIter—computing invariants of hyperbolic Coxeter groups, LMS J. Comput. Math. 18 (2015) 754 MR3434903
11 H C Im Hof, Napier cycles and hyperbolic Coxeter groups, Bull. Soc. Math. Belg. Sér. A 42 (1990) 523 MR1316209
12 A Kolpakov, B Martelli, Hyperbolic four-manifolds with one cusp, Geom. Funct. Anal. 23 (2013) 1903 MR3132905
13 A Kolpakov, L Slavich, Hyperbolic 4-manifolds, colourings and mutations, Proc. Lond. Math. Soc. (3) 113 (2016) 163 MR3534970
14 A Kolpakov, L Slavich, Symmetries of hyperbolic 4-manifolds, Int. Math. Res. Not. 2016 (2016) 2677 MR3519127
15 D D Long, A W Reid, On the geometric boundaries of hyperbolic 4-manifolds, Geom. Topol. 4 (2000) 171 MR1769269
16 G A Margulis, Discrete subgroups of semisimple Lie groups, 17, Springer (1991) MR1090825
17 G A Margulis, È B Vinberg, Some linear groups virtually having a free quotient, J. Lie Theory 10 (2000) 171 MR1748082
18 M Newman, Asymptotic formulas related to free products of cyclic groups, Math. Comp. 30 (1976) 838 MR466047
19 B E Nimershiem, All flat three-manifolds appear as cusps of hyperbolic four-manifolds, Topology Appl. 90 (1998) 109 MR1648306
20 J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (2019) MR4221225
21 J G Ratcliffe, S T Tschantz, Hyperbolic 24-cell 4-manifolds with one cusp, Exp. Math. 32 (2023) 269 MR4592946
22 E Rizzi, Some cusp-transitive hyperbolic 4-manifolds, Geom. Dedicata 219 (2025) 61 MR4916158
23 È B Vinberg, Hyperbolic reflection groups, Uspekhi Mat. Nauk 40 (1985) 29, 255 MR783604