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Geometric and arithmetic properties of Löbell polyhedra

Nikolay Bogachev and Sami Douba

Algebraic & Geometric Topology 25 (2025) 2281–2295
Bibliography
1 I Agol, Systoles of hyperbolic 4-manifolds, preprint (2006) arXiv:math/0612290
2 I Agol, M Belolipetsky, P Storm, K Whyte, Finiteness of arithmetic hyperbolic reflection groups, Groups Geom. Dyn. 2 (2008) 481 MR2442945
3 E M Andreev, On convex polyhedra in Lobachevsky spaces, Mat. Sb. 81 (1970) 445 MR259734
4 E M Andreev, On convex polyhedra of finite volume in Lobachevsky space, Mat. Sb. 83 (1970) 256 MR273510
5 O Antolín-Camarena, G R Maloney, R K W Roeder, Computing arithmetic invariants for hyperbolic reflection groups, from: "Complex dynamics" (editor D Schleicher), A K Peters (2009) 597 MR2508271
6 A Basmajian, Tubular neighborhoods of totally geodesic hypersurfaces in hyperbolic manifolds, Invent. Math. 117 (1994) 207 MR1273264
7 M V Belolipetsky, S A Thomson, Systoles of hyperbolic manifolds, Algebr. Geom. Topol. 11 (2011) 1455 MR2821431
8 R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer (1992) MR1219310
9 N Bergeron, F Haglund, D T Wise, Hyperplane sections in arithmetic hyperbolic manifolds, J. Lond. Math. Soc. 83 (2011) 431 MR2776645
10 N Bogachev, A Kolpakov, On faces of quasi-arithmetic Coxeter polytopes, Int. Math. Res. Not. 2021 (2021) 3078 MR4218347
11 W D Dunbar, G R Meyerhoff, Volumes of hyperbolic 3-orbifolds, Indiana Univ. Math. J. 43 (1994) 611 MR1291531
12 D Fisher, S Hurtado, A new proof of finiteness of maximal arithmetic reflection groups, Ann. H. Lebesgue 6 (2023) 151 MR4593607
13 T Gelander, Homotopy type and volume of locally symmetric manifolds, Duke Math. J. 124 (2004) 459 MR2084613
14 M Gromov, I Piatetski-Shapiro, Nonarithmetic groups in Lobachevsky spaces, Inst. Hautes Études Sci. Publ. Math. 66 (1988) 93 MR932135
15 M Gromov, W Thurston, Pinching constants for hyperbolic manifolds, Invent. Math. 89 (1987) 1 MR892185
16 R Kellerhals, A polyhedral approach to the arithmetic and geometry of hyperbolic link complements, J. Knot Theory Ramifications 32 (2023) 2350052 MR4626583
17 A Kolpakov, Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers, European J. Combin. 33 (2012) 1709 MR2950475
18 F Löbell, Beispiele geschlossener dreidimensionaler Clifford–Kleinscher Räume negativer Krümmung, Ber. Verh. Sächs Akad. Wiss. Leipzig Math.-Phys. Kl. 83 (1931) 167
19 C Maclachlan, A W Reid, The arithmetic of hyperbolic 3-manifolds, 219, Springer (2003) MR1937957
20 G A Margulis, Discrete subgroups of semisimple Lie groups, 17, Springer (1991) MR1090825
21 A D Mednykh, A Y Vesnin, Löbell manifolds revised, Sib. Èlektron. Mat. Izv. 4 (2007) 605 MR2465443
22 J S Meyer, C Millichap, R Trapp, Arithmeticity and hidden symmetries of fully augmented pretzel link complements, New York J. Math. 26 (2020) 149 MR4063955
23 G D Mostow, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 53 MR236383
24 V V Nikulin, Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces, Izv. Ross. Akad. Nauk Ser. Mat. 71 (2007) 55 MR2477273
25 M Phillips, S Levy, T Munzner, Geomview
26 G Prasad, Strong rigidity of Q-rank 1 lattices, Invent. Math. 21 (1973) 255 MR385005
27 R K W Roeder, J H Hubbard, W D Dunbar, Andreev’s theorem on hyperbolic polyhedra, Ann. Inst. Fourier (Grenoble) 57 (2007) 825 MR2336832
28 K Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan 29 (1977) 91 MR429744
29 S Thomson, Quasi-arithmeticity of lattices in PO(n,1), Geom. Dedicata 180 (2016) 85 MR3451458
30 A Y Vesnin, Three-dimensional hyperbolic manifolds of Löbell type, Sibirsk. Mat. Zh. 28 (1987) 50 MR924975
31 A Y Vesnin, Three-dimensional hyperbolic manifolds with a general fundamental polyhedron, Mat. Zametki 49 (1991) 29, 157 MR1135512
32 A Y Vesnin, Volumes of Löbell 3-manifolds, Mat. Zametki 64 (1998) 17 MR1694014
33 A Y Vesnin, Right-angled polytopes and three-dimensional hyperbolic manifolds, Uspekhi Mat. Nauk 72 (2017) 147 MR3635439
34 È B Vinberg, Discrete groups generated by reflections in Lobachevsky spaces, Mat. Sb. 72 (1967) 471 MR207853
35 È B Vinberg, Rings of definition of dense subgroups of semisimple linear groups, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971) 45 MR279206