The structure of groups with a quasiconvex hierarchy / Daniel T. Wise.

Format:

Book

Author/Creator:

Wise, Daniel T., 1971- author.

Series:

Annals of Mathematics Studies

Annals of Mathematics Studies ; 396

Language:

English

Subjects (All):

Hyperbolic groups.

Group theory.

Physical Description:

1 online resource (376 p.) : 166 color illus.

Place of Publication:

Princeton, New Jersey : Princeton University Press, [2021]

Language Note:

In English.

Summary:

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 generalizing 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.

Contents:

Frontmatter

Contents

Acknowledgments

Chapter One Introduction

Chapter Two CAT(0) Cube Complexes

Chapter Three Cubical Small-Cancellation Theory

Chapter Four Torsion and Hyperbolicity

Chapter Five New Walls and the B(6) Condition

Chapter Six Special Cube Complexes

Chapter Seven Cubulations

Chapter Eight Malnormality and Fiber-Products

Chapter Nine Splicing Walls

Chapter Ten Cutting X ∗

Chapter Eleven Hierarchies

Chapter Twelve Virtually Special Quotient Theorem

Chapter Thirteen Amalgams of Virtually Special Groups

Chapter Fourteen Large Fillings Are Hyperbolic and Preservation of Quasiconvexity

Chapter Fifteen Relatively Hyperbolic Case

Chapter Sixteen Largeness and Omnipotence

Chapter Seventeen Hyperbolic 3-Manifolds with a Geometrically Finite Incompressible Surface

Chapter Eighteen Limit Groups and Abelian Hierarchies

Chapter Nineteen Application Towards One-Relator Groups

Chapter Twenty Problems

References

Index

Notes:

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9780691213507

069121350X

OCLC:

1241449093