# Mathematics Colloquia and Seminars

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### Surfaces in finite covers of 3-manifolds: The virtual Haken conjecture

**Colloquium**

Speaker: | Nathan Dunfield, Harvard University |

Location: | 693 Kerr |

Start time: | Wed, Jan 15 2003, 4:10PM |

Haken 3-manifolds are those that contain topologically essential embedded surfaces. Haken manifolds are very well understood and most of the important questions in 3-manifold topology and geometry have been answered in this case. However, there are many 3-manifolds which are not Haken. For a non-Haken 3-manifold with infinite fundamental group, one can ask if it has a finite cover which is Haken. That such a manifold should always have a such a cover is the virtual Haken conjecture. I will broadly survey recent progress towards, and evidence for, this conjecture, after first giving some idea of why Haken manifolds are so "easy" to understand.

3:45 Refreshments will be served before the talk in 551 Kerr Hall