ON THE CLASSIFICATION OF ARITHMETIC GROUPS GENERATED BY REFLECTIONS IN LOBACHEVSKY SPACES

DOI10.1070/IM1982v018n01ABEH001385zbMath0477.22008MaRDI QIDQ3934723

Viacheslav V. Nikulin

Publication date: 1982

Published in: Mathematics of the USSR-Izvestiya (Search for Journal in Brave)

zbMATH Keywords

finitenessconvex polyhedronGalois latticesubgroup of finite indexLobachevsky spacehyperbolic quadratic formarithmetic group generated by reflections

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Polyhedra and polytopes; regular figures, division of spaces (51M20) Lattices and convex bodies (number-theoretic aspects) (11H06) Discrete subgroups of Lie groups (22E40) Special surfaces (14J25) General binary quadratic forms (11E16) Real algebraic and real-analytic geometry (14Pxx)

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The number of cusps of right-angled polyhedra in hyperbolic spaces ⋮ Correlations of length spectra for negatively curved manifolds ⋮ The classification of rank 3 reflective hyperbolic lattices over ⋮ Relatively hyperbolic Coxeter groups with maximal flats of codimension one ⋮ Cohomological rigidity of manifolds defined by 3-dimensional polytopes ⋮ Right-angled polyhedra and hyperbolic 3-manifolds ⋮ From geometry to arithmetic of compact hyperbolic Coxeter polytopes ⋮ Elliptic Fibrations on K3 Surfaces ⋮ \(K3\) surfaces of zero entropy admitting an elliptic fibration with only irreducible fibers ⋮ Bounds for arithmetic hyperbolic reflection groups in dimension 2 ⋮ Reflective Lorentzian lattices of signature \((5,1)\) ⋮ Notes on right-angled Coxeter polyhedra in hyperbolic spaces. ⋮ Reflective modular forms and applications ⋮ Classification of $(1{,}{\kern1pt}2)$-reflective anisotropic hyperbolic lattices of rank $4$

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