Structure of Groups with a Quasiconvex Hierarchy

<p>This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time including a cubical small-cancellation theory that generalizes ideas from the 1960s a version of Dehn Filling that functions in the category of special cube complexes and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams. <p/>The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds and validates this program in significant cases. Illustrated with more than 150 color figures this book will interest graduate students and researchers working in geometry algebra and topology.</p>