Coxeter Systems with Two-dimensional Davis-vinberg Complexes
نویسنده
چکیده
In this paper, we study Coxeter systems with two-dimensional DavisVinberg complexes. We show that for a Coxeter group W , if (W, S) and (W, S) are Coxeter systems with two-dimensional Davis-Vinberg complexes, then there exists S ⊂ W such that (W, S) is a Coxeter system which is isomorphic to (W, S) and the sets of reflections in (W, S) and (W, S) coincide. Hence the Coxeter diagrams of (W, S) and (W, S) have the same number of vertices, the same number of edges and the same multiset of edge-labels. This is an extension of results of A.Kaul and N.Brady, J.P.McCammond, B.Mühlherr and W.D.Neumann.
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Rigidity of Two-dimensional Coxeter Groups
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