The Structure of Groups with a Quasiconvex Hierarchy

By Daniel T Wise

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.

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.

• Format: Hardcover
• Language: English
• ISBN: 0691170444
• ISBN13: 9780691170442
• Release Date: May 2021
• Publisher: Princeton University Press
• Length: 376 Pages
• Weight: 1.59 lbs.
• Dimensions: 1.1" x 6.2" x 9.3"