PreprintBowditch's JSJ tree and the quasiisometry classification of certain Coxeter groupsPallavi Dani and Anne ThomasAbstractBowditch's JSJ tree for splittings over 2ended subgroups is a quasiisometry invariant for 1ended hyperbolic groups which are not cocompact Fuchsian. Our main result gives an explicit "visual" construction of this tree for certain hyperbolic rightangled 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 quasiisometry invariant. We also show that among the Coxeter groups we consider, the cocompact Fuchsian groups form a rigid quasiisometry class. This paper is available as a pdf (508kB) file.
