The structure of groups with a quasiconvex hierarchy - Number 209

"This monograph weaves together fundamentals of Mikhail Leonidovich Gromov's hyperbolic groups with the theory of cube complexes dual to spaces with walls.

Many fundamental new ideas and methodologies are presented here for the first time: A cubical small-cancellation theory generalizing ideas from the 1960's, a version of "Dehn Filling" that works in the category of special cube complexes, and a variety of new results about right-angled Artin groups.

The book culminates by providing an unexpected new theorem about the nature of hyperbolic groups that are constructible as amalgams.

Among the stunning applications, are the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of R.J.

Baumslag's conjecture on the residual finiteness of one-relator groups with torsion.

Most importantly, the book outlines the author's program towards the resolution of the most important remaining conjectures of William Thurston, and achieves