Structure of Groups with a Quasiconvex Hierarchy: (AMS-209)

This monograph presents groundbreaking ideas and methodologies in geometric group theory and 3-manifold topology,including a cubical small-cancellation theory,a Dehn Filling version,and results about right-angled Artin groups. It also establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds and validates it in significant cases.

\n Format: Paperback / softback
\n Length: 376 pages
\n Publication date: 04 May 2021
\n Publisher: Princeton University Press
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This groundbreaking monograph delves into the realm of geometric group theory and 3-manifold topology, presenting a series of innovative ideas and methodologies. Among these, the author introduces a cubical small-cancellation theory that expands upon concepts from the 1960s, develops a version of Dehn filling tailored for special cube complexes, and explores various results related to right-angled Artin groups. The culmination of this work is a remarkable theorem that sheds light on the nature of hyperbolic groups that can be constructed as amalgams.

The applications explored in this monograph are diverse and impactful. One notable application involves the virtual fibering of cusped hyperbolic 3-manifolds, a technique that enhances the understanding and study of these complex structures. Additionally, the author resolves Baumslag's conjecture on the residual finiteness of one-relator groups with torsion, a significant breakthrough in the field of group theory.

Perhaps the most significant contribution of this work is the establishment of a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds. This program employs cutting-edge techniques and provides a rigorous framework for tackling these challenging problems. By validating this program in significant cases, the author has made substantial progress toward unraveling the mysteries of hyperbolic 3-manifolds.

Throughout the monograph, the author employs clear and concise explanations, accompanied by numerous illustrative color figures. This book is designed to appeal to graduate students and researchers in geometry, algebra, and topology, offering a comprehensive and up-to-date exploration of the field.

In summary, this monograph represents a significant breakthrough in the fields of geometric group theory and 3-manifold topology. Through the introduction of novel ideas, methodologies, and theorems, the author has paved the way for further advancements in these areas. The applications described herein have the potential to revolutionize our understanding of hyperbolic 3-manifolds and other related structures. With its comprehensive coverage, engaging writing style, and wealth of visual aids, this book is an invaluable resource for scholars and researchers alike.

\n Weight: 614g\n
Dimension: 155 x 235 x 26 (mm)\n
ISBN-13: 9780691170459\n \n