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Coxeter Decompositions of Hyperbolic Polygons

โœ Scribed by A.A. Felikson

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
272 KB
Volume
19
Category
Article
ISSN
0195-6698

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โœฆ Synopsis

Let P be a polygon on hyperbolic plane H 2 . A Coxeter decomposition of a polygon P is a nontrivial decomposition of P into finitely many Coxeter polygons F i , such that any two polygons F 1 and F 2 having a common side are symmetric with respect to this common side. In this paper we classify the Coxeter decompositions of triangles, quadrilaterals and ideal polygons.

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Assume that the nerve K of a hyperbolic Coxeter group ฮ“ is n-connected and the complement K \ โˆ† to every simplex is n-connected. Then the boundary โˆ‚ฮ“ is n-connected and locally nconnected.