# Geometry and Topology Down Under

Share this page *Edited by *
*Craig D. Hodgson; William H. Jaco; Martin G. Scharlemann; Stephan Tillmann*

The main topic of the book is low-dimensional geometry and
topology. It includes both survey articles based on courses presented
at the conferences and research articles devoted to important
questions in low-dimensional geometry. Together, these contributions
show how methods from different fields of mathematics contribute to
the study of 3-manifolds and Gromov hyperbolic groups. It also
contains a list of favorite problems by Hyam Rubinstein.

# Table of Contents

## Geometry and Topology Down Under

- Preface vii8 free
- The Hyamfest ix10 free
- Courses at the Hyamfest xi12 free
- Talks at the Hyamfest xiii14 free
- Biographical Sketch of Hyam Rubinstein xxi22 free
- What is an Almost Normal Surface? 124 free
- The Ergodic Theory of Hyperbolic Groups 1538
- Mapping Class Groups of 3-Manifolds, Then and Now 5376
- Stacks of Hyperbolic Spaces and Ends of 3-Manifolds 6588
- Harmonic Maps and Integrable Systems 139162
- Some of Hyam’s Favourite Problems 165188
- Almost Normal Surfaces with Boundary 177200
- 1. Introduction 177200
- 2. Compressing Disks and Disk Complexes 178201
- 3. The 1-skeleton: [𝒞(ℋ)] and [𝒞ℬ(ℋ)] disconnected implies [𝒞ℰ(ℋ,𝒯¹)] is disconnected 181204
- 4. The 2-skeleton: [𝒞ℰ(ℋ,𝒯¹)] disconnected implies [𝒞ℰ(ℋ,𝒯²)] is disconnected. 186209
- 5. The 3-skeleton: [𝒞ℰ(ℋ,𝒯²)] disconnected implies ℋ is almost normal 189212
- References 193216

- Computational Topology with Regina: Algorithms, Heuristics and Implementations 195218
- Left-Orderability and Exceptional Dehn Surgery on Two-Bridge Knots 225248
- Networking Seifert Surgeries on Knots IV: Seiferters and Branched Coverings 235258
- Commensurability of Knots and 𝐿²–Invariants 263286
- The Groups of Fibred 2-Knots 281304
- On the Number of Hyperbolic 3-Manifolds of a Given Volume 295318
- 1. Introduction 295318
- 2. Hyperbolic Dehn fillings determined by their volumes 299322
- 3. Dehn filling on the figure eight knot complement and its sister 302325
- 4. Dehn filling on the Whitehead link complement and its sister 304327
- 5. Higher order terms in the Neumann-Zagier asymptotic formula 307330
- 6. Hyperbolic graphs with parabolic meridians 309332
- 7. Associated circle packings and cusp moduli 312335
- 8. Construction of different manifolds sharing the same volume 315338
- 9. Some Open Questions 317340
- References 318341

- Seifert Fibered Surgery and Rasmussen Invariant 321344
- Existence of Spherical Angle Structures on 3-Manifolds 337360
- 3-Manifolds with Heegaard Splittings of Distance Two 341364
- Generating the Genus 𝑔+1 Goeritz Group of a Genus 𝑔 Handlebody 347370