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A 'transversal' for minimal invariant sets in the boundary of a CAT(0) group
2012
Transactions of the American Mathematical Society
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We introduce new techniques for studying boundary dynamics of CAT(0) groups. For a group G acting geometrically on a CAT(0) space X we show there is a flat F ⊂ X of maximal dimension (denote it by d), whose boundary sphere intersects every minimal G-invariant subset of ∂ ∞ X. As applications we obtain an improved dimension-dependent bound diam ∂ T X ≤ 2π − arccos − 1 d + 1 on the Tits-diameter of ∂X for non-rank-one groups, a necessary and sufficient dynamical condition for G to be virtually
doi:10.1090/s0002-9947-2012-05714-x
fatcat:pa2edi3ilvctjedh3gsmazlkbi