# Mathematics Colloquia and Seminars

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### Automatic groups and displacement estimates for hyperbolic manifolds.

**Geometry/Topology**

Speaker: | Bryan Mosher, University of Michigan |

Location: | 693 Kerr |

Start time: | Wed, Feb 24 1999, 4:10PM |

A technique will be described which uses an algebraic decomposition of a Kleinian group to find bounds on the displacement of points in hyperbolic space by distinguished isometries in the group. Combinatorial data,encoded by an automatic structure for the Kleinian group, is converted into the geometric estimates via the construction due to Patterson and Sullivan of measures on the sphere at infinity of hyperbolic space. A prototype forthe results is the Log 3 Theorem of Culler and Shalen, which treats rank-2 free Kleinian groups. An application to Fuchsian groups will also be presented.