# Mathematics Colloquia and Seminars

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### 3-manifolds, essential laminations and group actions

**Geometry/Topology**

Speaker: | Sergio Fenley, Florida State University |

Location: | 693 Kerr |

Start time: | Wed, May 5 2004, 4:10PM |

Three-manifolds with esssential laminations have very good properties, for example it is easy to prove that they are irreducible and have universal cover R^3. As such it is important to characterize which 3-manifolds have essential laminations. Suppose that a 3-manifold M has an essential lamination L. The lifted lamination L~ to the universal cover has a "leaf space", which after a couple of possible modifications turns into a tree with a non trivial group action of the fundamental group of M on it. One can then analyse such 1-dimensional dynamical systems on a tree for particular groups. Some specific cases associated to Dehn surgery on torus bundles over the circle yield examples of hyperbolic 3-manifolds without essential laminations.