The Structure of Groups with a Quasiconvex Hierarchy
eBook - PDF

The Structure of Groups with a Quasiconvex Hierarchy

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

The Structure of Groups with a Quasiconvex Hierarchy

About this book

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.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access The Structure of Groups with a Quasiconvex Hierarchy by Daniel T. Wise in PDF and/or ePUB format, as well as other popular books in Mathematics & Geometry. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Contents
  3. Acknowledgments
  4. 1. Introduction
  5. 2. CAT(0) Cube Complexes
  6. 3. Cubical Small-Cancellation Theory
  7. 4. Torsion and Hyperbolicity
  8. 5. New Walls and the B(6) Condition
  9. 6. Special Cube Complexes
  10. 7. Cubulations
  11. 8. Malnormality and Fiber-Products
  12. 9. Splicing Walls
  13. 10. Cutting X*
  14. 11. Hierarchies
  15. 12. Virtually Special Quotient Theorem
  16. 13. Amalgams of Virtually Special Groups
  17. 14. Large Fillings Are Hyperbolic and Preservation of Quasiconvexity
  18. 15. Relatively Hyperbolic Case
  19. 16. Largeness and Omnipotence
  20. 17. Hyperbolic 3-Manifolds with a Geometrically Finite Incompressible Surface
  21. 18. Limit Groups and Abelian Hierarchies
  22. 19. Application Towards One-Relator Groups
  23. 20. Problems
  24. References
  25. Index