Book contents
- Frontmatter
- Contents
- Preface
- Part One LECTURES
- Part Two Expository Articles
- Part Three Research Articles
- 6 A counterexample to questions about boundaries, stability, and commensurability
- 7 A note on the acylindrical hyperbolicity of groups acting on CAT(0) cube complexes
- 8 Immutability is not uniformly decidable in hyperbolic groups
- 9 Sphere systems, standard form, and cores of products of trees
9 - Sphere systems, standard form, and cores of products of trees
from Part Three - Research Articles
Published online by Cambridge University Press: 22 June 2019
Book contents
- Frontmatter
- Contents
- Preface
- Part One LECTURES
- Part Two Expository Articles
- Part Three Research Articles
- 6 A counterexample to questions about boundaries, stability, and commensurability
- 7 A note on the acylindrical hyperbolicity of groups acting on CAT(0) cube complexes
- 8 Immutability is not uniformly decidable in hyperbolic groups
- 9 Sphere systems, standard form, and cores of products of trees
Summary
We introduce the concept of a standard form for two embedded maximal sphere systems in the doubled handlebody, and we prove an existence and uniqueness result. In particular, we show that pairs of maximal sphere systems in the doubled handlebody (up to homeomorphism) bijectively correspond to square complexes satisfying a set of properties. This work is a variant on Hatcher's normal form.
- Type
- Chapter
- Information
- Beyond Hyperbolicity , pp. 186 - 222Publisher: Cambridge University PressPrint publication year: 2019