Asymptotic behavior of word metrics on Coxeter groups.
Summary: We study the geometry of tessellation defined by the walls in the Moussong complex \(\mathcal M_W\) of a Coxeter group \(W\). It is proved that geodesics in \(\mathcal M_W\) can be approximated by geodesic galleries of the tessellation. A formula for the translation length of an element of \(W\) is given. We prove that the restriction of the word metric on the \(W\) to any free Abelian subgroup \(A\) is Hausdorff equivalent to a regular norm on \(A\).
scientific article; zbMATH DE number 5947057