Quasi-isometry invariance of group splittings

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A new proof of Gromov's theorem on groups of polynomial growth (2007, methodology): “There are several important applications of the WilkieVan Den Dries refinement [vdDW84] of Gromov’s theorem [Gro81] that do not follow from the original statement; for instance [Pap05], or the theorem of Varopoulos that a group satisfies a d-dimensional Euclidean isoperimetric inequality unless it i”
Boundaries and JSJ Decompositions of CAT(0)-Groups (2007, background): “We remark that in case ∂X is locally connected the theorem above follows from [20].”
Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity (2005, background): “In [37,53,67,68,75] strong quasi-isometric rigidity results are proved for some particular cases of weakly relatively hyperbolic groups—in fact all of them are fundamental groups of some graphs of groups (fundamental groups of Haken manifolds, groups with a JSJ decomposition, fundamental groups of f”
Geometry and rigidity of mapping class groups (2008, background): “• Graphs of n-dimensional Poincaré duality groups, for some fixed n (Farb-Mosher, Whyte, Mosher-Sageev-Whyte, Papasoglu [18, 19, 45, 46, 49, 56]).”