## Geometric Methods in Group Theory: AMS Special Session Geometric Group Theory, October 5-6, 2002, Northeastern University, Boston, Massachusetts : Special Session at the First Joint Meeting of the American Mathematical Society and the Real Sociedad Matemática Española, June 18-21, 2003, Seville, SpainThis volume presents articles by speakers and participants in two AMS special sessions, Geometric Group Theory and Geometric Methods in Group Theory, held respectively at Northeastern University (Boston, MA) and at Universidad de Sevilla (Spain). The expository and survey articles in the book cover a wide range of topics, making it suitable for researchers and graduate students interested in group theory. |

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### Contents

1 | |

a survey | 11 |

Characterizing rigid simplicial actions on trees | 27 |

Improving an algorithm to solve multiple simultaneous conjugacy problems in braid groups | 35 |

On singular Artin monoids | 43 |

A surface groups analogue of a theorem of Magnus | 59 |

Shift automorphisms of finite order | 71 |

Counting primitive elements of a free group | 91 |

Thompsons group F is maximally nonconvex | 131 |

Seesaw words in Thompsons group F | 147 |

Piecewiseprojective representation of Thompsons group T | 161 |

Bijective quasiisometries of amenable groups | 181 |

On definitions of relatively hyperbolic groups | 189 |

Embedding wreathlike products in finitely presented groups I | 197 |

Metric properties of the lamplighter group as an automata group | 207 |

An example of noncontracting weakly branch automaton group | 219 |

A rank formula for amalgamated products with finite amalgam | 99 |

A simple proof of a theorem of Karrass and Solitar | 107 |

Distortion functions and the membership problem for submonoids of groups and monoids | 109 |

Travelling salesman problem in groups | 225 |

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### Common terms and phrases

A-tree abelian group action Algebra algorithm amalgamated Artin groups automata generating set automorphism bijection braid groups caret Cayley graph compute conjugate convex Corollary cursor cyclic defined definition denote edge group embedding finitely generated group finitely presented group forest diagram free group free product geodesic geometric given graded monoid graph of groups group G group theory Hence HNN-extension homomorphism horoballs horocycle hyperbolic groups illuminated bulbs isometric Lemma length function Let G Math membership problem metric minimal length representatives Mon(S normal closure normal form Note one-relator groups path polynomial prefixes properly 3-realizable Proposition prove quasi-isometry quotient recursively reduced respect seesaw words sequence shift automorphism singular Artin monoids solvable space subgroup submonoid subset Suppose Teichmüller space Thompson's group tree pair diagram upper distortion function vertices word length word problem wreath product