Geodesic
Asymptotic behavior of word metrics on Coxeter groups.
Documenta mathematica, Tome 16 (2011), pp. 373-398
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We study the geometry of tessellation defined by the walls in the Moussong complex MW​ of a Coxeter group W. It is proved that geodesics in MW​ 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.
DOI : 10.4171/dm/335
Classification : 20F55, 51F15
Mots-clés : Coxeter group, moussong complex, translation length 
@article{10_4171_dm_335,
     author = {G.A. Noskov},
     title = {Asymptotic behavior of word metrics on {Coxeter} groups.},
     journal = {Documenta mathematica},
     pages = {373--398},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/335},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/335/}
}
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G.A. Noskov. Asymptotic behavior of word metrics on Coxeter groups.. Documenta mathematica, Tome 16 (2011), pp. 373-398. doi: 10.4171/dm/335

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