Geodesic
Coxeter group in Hilbert geometry
Ludovic Marquis1 orcid
1Université de Rennes I, France
Groups, geometry, and dynamics, Tome 11 (2017) no. 3, pp. 819-877

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DOI

A theorem of Tits and Vinberg allows to build an action of a Coxeter group €Γ on a properly convex open set Ω of the real projective space, thanks to the data P of a polytope and reflection across its facets. We give sufficient conditions for such action to be of finite covolume, convex-cocompact or geometrically finite. We describe a hypothesis that makes those conditions necessary.
DOI : 10.4171/ggd/416
Classification : 20-XX, 53-XX
Mots-clés : Coxeter group, Hilbert geometry, Discrete subgroup of Lie group, convex projective structure on manifold and orbifold, geometric group theory

Ludovic Marquis  1

1 Université de Rennes I, France 
Ludovic Marquis. Coxeter group in Hilbert geometry. Groups, geometry, and dynamics, Tome 11 (2017) no. 3, pp. 819-877. doi: 10.4171/ggd/416
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     title = {Coxeter group in {Hilbert} geometry},
     journal = {Groups, geometry, and dynamics},
     pages = {819--877},
     year = {2017},
     volume = {11},
     number = {3},
     doi = {10.4171/ggd/416},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/416/}
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