The Structure of Groups with a Quasiconvex Hierarchy: (Ams-209) (Paperback) (ISBN-13: 9780691170459)

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.

Author: Daniel T. Wise
ISBN-10: 0691170452
ISBN-13: 9780691170459
Publisher: Princeton University Press
Language: English
Published: 05/04/2021
Pages: 376
Format: Paperback
Weight: 1.35lbs
Size: 9.20h x 6.10w x 1.10d