Geodesic
Asymptotic behavior of word metrics on Coxeter groups.
Documenta mathematica, Tome 16 (2011), pp. 373-398.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the geometry of tessellation defined by the walls in the Moussong complex $\calm_W$ of a Coxeter group $W$. It is proved that geodesics in $\calm_W$ 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 $A.$
Classification : 20F55, 51F15
Keywords: Coxeter group, moussong complex, translation length 
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     author = {Noskov, G.A.},
     title = {Asymptotic behavior of word metrics on {Coxeter} groups.},
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     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a23/}
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Noskov, G.A. Asymptotic behavior of word metrics on Coxeter groups.. Documenta mathematica, Tome 16 (2011), pp. 373-398. http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a23/