** "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.