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Discrete reflection groups in Lobachevskij spaces of high dimension. (Russian) Zbl 0539.51005

It is proved that in Lobachevskij space of dimension \(n\geq 62\) there exist no discrete reflection groups with a bounded fundamental polyhedron. The proof is based on recent results on combinatorics of simplicial convex polyhedra. A more careful analysis carried out in another work of the author [VINITI Dep. No.3417-82] enables one to prove the same for \(n\geq 30\).

MSC:

51F15 Reflection groups, reflection geometries
20H15 Other geometric groups, including crystallographic groups
51M10 Hyperbolic and elliptic geometries (general) and generalizations
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