Hyperbolic geometry and reflection groups
نویسندگان
چکیده
منابع مشابه
Arithmetic Hyperbolic Reflection Groups
A hyperbolic reflection group is a discrete group generated by reflections in the faces of an n-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis on the results that were obtained in the last ten years and on the open problems.
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The goal of this paper is twofold. First, it consists of an introduction to the basic features of hyperbolic geometry, and the geometry of an important class of functions of the hyperbolic plane, isometries. Second, it identifies a group structure in the set of isometries, specifically those that preserve orientation, and deals with the topological properties of their discrete subgroups. In the...
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We consider the automorphism groups of various Lorentzian lattices over the Eisenstein, Gaussian, and Hurwitz integers, and in some of them we find reflection groups of finite index. These provide new finitecovolume reflection groups acting on complex and quaternionic hyperbolic spaces. Specifically, we provide groups acting on CH for all n < 6 and n = 7, and on HH for n = 1, 2, 3, and 5. We co...
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or perhaps with the face of our mother or father. We quickly learn to identify the axis of symmetry and know intuitively that an object is symmetric if it “the same” on both sides of this axis. In mathematics symmetry is abundant and takes many forms. Symmetry like that of the butterfly or a face is referred to as reflexive symmetry. Any line in the plane determines a unique symmetry which refl...
متن کاملFiniteness of Arithmetic Hyperbolic Reflection Groups
We prove that there are only finitely many conjugacy classes of arithmetic maximal hyperbolic reflection groups.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1996
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700016853