Offering an alternative proof of the Bestvina-Feighn theorem for trees of hyperbolic spaces, the work defines uniform quasigeodesics and demonstrates Cannon-Thurston maps for subtrees and relatively hyperbolic spaces. It probes laminations and discusses key group-theoretic outcomes.
This book offers an alternative proof of the Bestvina-Feighn combination theorem for trees of hyperbolic spaces and describes uniform quasigeodesics in such spaces. As one of the applications of their description of uniform quasigeodesics, the authors prove the existence of Cannon-Thurston maps for inclusion maps of total spaces of subtrees of hyperbolic spaces and of relatively hyperbolic spaces. They also analyze the structure of Cannon-Thurston laminations in this setting. Furthermore, some group-theoretic applications of these results are discussed. This book also contains background material on coarse geometry and geometric group theory.