** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2016.01.12, 15:00–17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "Cutpoints of CAT(0) groups."

**Speaker:** Panos
Papazoglou (University of Oxford)

**Abstract:**
It is known that if the boundary of a 1–ended
hyperbolic group \(G\) has a local cut point then \(G\) splits over a 2–ended group. We prove a similar theorem for CAT(0)
groups, namely that if a finite set of points separates the boundary
of a 1–ended CAT(0) group \(G\)
then \(G\) splits over a 2–ended group. Along the way we prove two results of independent interest: we show that continua separated
by finite sets of points admit a tree-like decomposition and we show a splitting theorem for nesting actions on \(\mathbb{R}\)–trees.
This is joint work with Eric Swenson.