arXiv subjects

Eric L. Swenson

Publications and source records attributed to Eric L. Swenson.

2 recordsLinked to original sources

arXiv2011

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 $\partial_\infty X$. 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.

math.GR↗

arXiv2005

Bootstrapping in convergence groups

We prove a true bootstrapping result for convergence groups acting on a Peano continuum. We give an example of a Kleinian group H which is the amalgamation of two closed hyperbolic surface groups along a simple closed curve. The limit set Lambda H is the closure of a `tree of circles' (adjacent circles meeting in pairs of points). We alter the action of H on its limit set such that H no longer acts as a convergence group, but the stabilizers of the circles remain unchanged, as does the action of a circle stabilizer on said circle. This is done by first separating the circles and then gluing them together backwards.

math.GR↗