On Geometric Flats in the CAT(0) Realization of Coxeter Groups and Tits Buildings

DOI10.4153/CJM-2009-040-8zbMath1231.20034arXivmath/0607741OpenAlexW2073673928MaRDI QIDQ5322975

Pierre-Emmanuel Caprace, Frédéric Haglund

Publication date: 23 July 2009

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607741

zbMATH Keywords

Coxeter groupsCAT(0) spacesgeometric actionsbuildingsfree Abelian subgroupsGromov-hyperbolic groupsconvex cocompact subgroupsflat rank

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Buildings and the geometry of diagrams (51E24) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Groups with a (BN)-pair; buildings (20E42) Reflection groups, reflection geometries (51F15)

Related Items (19)

CAT(0) cube complexes with flat hyperplanes ⋮ Scale and tidy subgroups for Weyl-transitive automorphism groups of buildings ⋮ Buildings and Kac-Moody Groups ⋮ Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls. ⋮ Non-hyperbolic automatic groups and groups acting on CAT(0) cube complexes ⋮ Hyperbolicities in CAT(0) cube complexes ⋮ CAT(0) spaces with boundary the join of two Cantor sets. ⋮ Combinatorial and group-theoretic compactifications of buildings ⋮ Unnamed Item ⋮ On the coarse-geometric detection of subgroups. ⋮ Hyperbolic diagram groups are free ⋮ Hyperbolic groups have flat-rank at most 1 ⋮ A lattice in more than two Kac-Moody groups is arithmetic. ⋮ Rank-one isometries of buildings and quasi-morphisms of Kac-Moody groups. ⋮ Algebraic characterisation of relatively hyperbolic special groups ⋮ Non-distortion of twin building lattices. ⋮ Decomposing locally compact groups into simple pieces ⋮ Simplicity and superrigidity of twin building lattices. ⋮ Some remarks on proper actions, proper metric spaces, and buildings

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