Rigidity of two-dimensional Coxeter groups

Details Rigidity of two-dimensional Coxeter groups Rigidity of two-dimensional Coxeter groups

2003-11-12

arxiv.org/abs/math/0311177v2

Mathematics

Group Theory

30 pages, 3 figures. Replacement corrects an error in content

Scientific paper

A Coxeter system is called two-dimensional if its associated Davis complex is two-dimensional (equivalently, every spherical subgroup has rank less than or equal to 2). We prove that given a two-dimensional system (W,S) and any other system (W,S') which yields the same reflections, the diagrams corresponding to these systems are isomorphic, up to the operation of diagram twisting defined by N. Brady, J. McCammond, B. Muhlherr, and W. Neumann. As a step in the proof of this result, certain two-dimensional groups are shown to be reflection rigid in the sense defined by the above authors, and a result concerning the strong rigidity of two-dimensional systems is given in the final section.

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