Bernhard Kron (Universitat Wien)
Linear boundary of finitely generated groups
We introduce a boundary for metric space with respect to a chosen family of unbounded subsets which generalizes
Tits' boundary of Cat(0)-space. In the word metric of finitely generated groups this boundary does not depend on the
choice of generators (letters). For example, the boundary of the free abelian group of rank $d$ is the $(d-1)$-dimensional sphere.
For nilpotent groups we obtain a disjoint union of spheres whose dimensions correspond to the free ranks of the abelian quotients in the central series.
We also discuss some interesting distorsion-phenomena in HNN-extensions with respect to this boundary.
Joint work with J. Lehnert, E.Teufl, N. Seifter and M. Stein.