"Geometry and Analysis on Groups" Research Seminar

Time: 2015.04.14, 15:00--17:00
Location: Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Quasi-isometry classification of certain hyperbolic right-angled Coxeter groups."
Speaker: Anne Thomas (University of Glasgow)
Abstract: Let $$\Gamma$$ be a finite simple graph. The associated right-angled Coxeter group $$W_\Gamma$$ has generating set $$S$$ the vertices of $$\Gamma$$, with relations $$s^2 = 1$$ for all generators $$s$$, and generators $$s$$ and $$t$$ commuting if and only if there is an edge $$\{s,t\}$$. Results of Moussong and Davis characterise the $$W_\Gamma$$ which are one-ended and hyperbolic in terms of the defining graph $$\Gamma$$. Bowditch's JSJ tree is a quasi-isometry invariant for one-ended hyperbolic groups, and our main results give an explicit algorithm for constructing this tree for the groups $$W_\Gamma$$ when $$\Gamma$$ is triangle-free. We then use our description to show that the JSJ tree is a complete quasi-isometry invariant for the subclass of groups such that $$\Gamma$$ does not contain a subdivided $$K_4$$ subgraph.