Wednesday, 3 August, 14:45-15:45, Room 4102


Eric Swenson (Brigham Young University)


A Transversal for Minimal Invariant Sets in the Boundary of a
CAT(0) Group


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 $F\subset X$ of maximal
dimension whose boundary sphere intersects every minimal $G$-invariant
subset of $\partial X$. As a result we derive a necessary and
sufficient dynamical condition for $G$ to be virtually-Abelian, as
well as a new approach to Ballmann's rank rigidity conjecture.

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