Rigidity of Right-angled Coxeter Groups
نویسندگان
چکیده
In mathematics, a group is the set of symmetries of an object. Coxeter groups are a broad and natural class of groups that are related to reflectional symmetries. Each Coxeter group is determined by a diagram, called a labeled graph, that encodes algebraic information about the group. In general, two different labeled graphs can give rise to the same group. It is therefore natural to ask: are there classes of Coxeter groups that have unique associated graphs? Coxeter groups that have a unique labeled graph are said to be rigid. There are important classes of Coxeter groups that are rigid. Radcliffe [5] showed that the class of right-angled Coxeter groups is rigid, and Bahls [1] extended this result to the class of even Coxeter groups. The main aim of this thesis is to provide an alternative proof, based on an argument outlined by A. Piggott [4], of the rigidity of right-angled Coxeter groups. RIGIDITY OF RIGHT-ANGLED COXETER GROUPS 1
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