## Geometry and Topology Down Under Craig D. Hodgson, William H. Jaco, Martin G. Scharlemann, Stephan Tillmann This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11-22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein. 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. |

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### Contents

What is an Almost Normal Surface? | 1 |

The Ergodic Theory of Hyperbolic Groups | 15 |

Mapping Class Groups of 3Manifolds Then and Now | 53 |

Stacks of Hyperbolic Spaces and Ends of 3Manifolds | 65 |

Harmonic Maps and Integrable Systems | 139 |

Some of Hyams Favourite Problems | 165 |

Almost Normal Surfaces with Boundary | 177 |

Algorithms Heuristics and Implementations | 195 |

Seiferters and Branched Coverings | 235 |

Commensurability of Knots and ²Invariants | 263 |

The Groups of Fibred 2Knots | 281 |

On the Number of Hyperbolic 3Manifolds of a Given Volume | 295 |

Seifert Fibered Surgery and Rasmussen Invariant | 321 |

Existence of Spherical Angle Structures on 3Manifolds | 337 |

3Manifolds with Heegaard Splittings of Distance Two | 341 |

Generating the Genus +1 Goeritz Group of a Genus Handlebody | 347 |