Bowditch's JSJ tree and the quasi-isometry classification of certain Coxeter groups

Pallavi Dani and Anne Thomas

Abstract

Bowditch's JSJ tree for splittings over 2-ended subgroups is a quasi-isometry invariant for 1-ended hyperbolic groups which are not cocompact Fuchsian. Our main result gives an explicit "visual" construction of this tree for certain hyperbolic right-angled Coxeter groups. As an application of our construction we identify a large class of such groups for which the JSJ tree, and hence the visual boundary, is a complete quasi-isometry invariant. We also show that among the Coxeter groups we consider, the cocompact Fuchsian groups form a rigid quasi-isometry class.