Surfaces, 3-manifolds, and character varieties

Document Type

Presentation Abstract

Presentation Date

3-4-2008

Abstract

The geometry and topology of a surface can be understood by cutting it along essential curves. The success of this approach to surfaces has motivated a similar approach in dimension 3. In this setting, instead of looking for essential curves in a 2-dimensional space, we are interested in essential surfaces in a 3-dimensional space.

Essential surfaces are difficult to find - many manifolds do not contain any - and finding them is a fundamental difficulty in 3-manifold topology. The character variety and machinery of Culler and Shalen provides one of the best ways to find these surfaces. Their work was critical in many of the most important achievements in 3-manifold topology over the last 35 years.

I will introduce their techniques and talk about two related questions that I have answered in my research.

Additional Details

Monday, 4 March 2008
4:10 p.m. in Math 103
3:30 p.m. Refreshments in Math Lounge 109

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