On geometric flats in CAT(0) realization of Coxeter groups and Tits buildings
(2009) Canadian Journal of Mathematics — Vol. 61, n° 4, p. 740-761 (2009)
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- Abstract
- Given a complete CAT(0) space endowed with a geometric action of a group , it is known that if contains a free abelian group of rank , then contains a geometric flat of dimension . We prove the converse of this statement in the special case where is a convex subcomplex of the CAT(0) realization of a Coxeter group , and is a subgroup of . In particular a convex cocompact subgroup of a Coxeter group is Gromov-hyperbolic if and only if it does not contain a free abelian group of rank 2. Our result also provides an explicit control on geometric flats in the CAT(0) realization of arbitrary Tits buildings.
- Affiliations
Orsay Département de mathématiques
Citations
Caprace, P.-E., & Haglund, F. (2009). On geometric flats in CAT(0) realization of Coxeter groups and Tits buildings. Canadian Journal of Mathematics, 61(4), 740-761. https://doi.org/10.4153/CJM-2009-040-8 (Original work published 2009)