"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.