Abstract:
It is proved that there do not exist discrete arithmetic groups generated by reflections in Lobachevsky spaces if the dimension of the Lobachevsky space is greater than 15 and the degree of the ground field is sufficiently large.
Bibliography: 24 titles.
Citation:
V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123
\Bibitem{Nik81}
\by V.~V.~Nikulin
\paper On the classification of arithmetic groups generated by reflections in Lobachevsky spaces
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 1
\pages 99--123
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https://doi.org/10.1070/IM1982v018n01ABEH001385
https://www.mathnet.ru/eng/im/v45/i1/p113
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N. V. Bogachev, “Classification of (1,2)-reflective anisotropic hyperbolic lattices of rank 4”, Izv. Math., 83:1 (2019), 1–19
Gritsenko V. Nikulin V.V., “Lorentzian Kac-Moody Algebras With Weyl Groups of 2-Reflections”, Proc. London Math. Soc., 116:3 (2018), 485–533
Mark A., “The Classification of Rank 3 Reflective Hyperbolic Lattices Over Z[Root 2]”, Math. Proc. Camb. Philos. Soc., 164:2 (2018), 221–257
Linowitz B., “Bounds For Arithmetic Hyperbolic Reflection Groups in Dimension 2”, Transform. Groups, 23:3 (2018), 743–753
V. A. Gritsenko, “Reflective modular forms and applications”, Russian Math. Surveys, 73:5 (2018), 797–864
Turkalj I., “Reflective Lorentzian Lattices of Signature (5,1)”, J. Algebra, 513 (2018), 516–544
N. V. Bogachev, “Reflective anisotropic hyperbolic lattices of rank 4”, Russian Math. Surveys, 72:1 (2017), 179–181
V. M. Buchstaber, N. Yu. Erokhovets, M. Masuda, T. E. Panov, S. Park, “Cohomological rigidity of manifolds defined by 3-dimensional polytopes”, Russian Math. Surveys, 72:2 (2017), 199–256
A. Yu. Vesnin, “Right-angled polyhedra and hyperbolic 3-manifolds”, Russian Math. Surveys, 72:2 (2017), 335–374
Nonaka J., “The Number of Cusps of Right-angled Polyhedra in Hyperbolic Spaces”, Tokyo J. Math., 38:2 (2015), 539–560
Belolipetsky M. Linowitz B., “On Fields of Definition of Arithmetic Kleinian Reflection Groups II”, Int. Math. Res. Notices, 2014, no. 9, 2559–2571
V.V.. Nikulin, “Elliptic Fibrations On K3 Surfaces”, Proceedings of the Edinburgh Mathematical Society, 2013, 1
Mark Pollicott, Richard Sharp, “Correlations of Length Spectra for Negatively Curved Manifolds”, Commun. Math. Phys, 2012
Maclachlan C., “Bounds for discrete hyperbolic arithmetic reflection groups in dimension 2”, Bull London Math Soc, 43:1 (2011), 111–123
Viacheslav V. Nikulin, “Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups”, Proc. Steklov Inst. Math., 273 (2011), 229–237
V. V. Nikulin, “The transition constant for arithmetic hyperbolic reflection groups”, Izv. Math., 75:5 (2011), 971–1005
Maclachlan C., “Commensurability classes of discrete arithmetic hyperbolic groups”, Groups Geom Dyn, 5:4 (2011), 767–785
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