- Sponsor
- Department of Mathematics
- Speaker
- Brevan Ellefsen
- Cost
- n/a
- Contact
- Anthony D'Arienzo
- apd6@illinois.edu
- Views
- 20
- Originating Calendar
- Graduate Student Seminars in Mathematics
- Speaker: Brevan Ellefsen
- Introduction to Haken Manifolds
In dimension 2, surfaces are commonly classified by cutting and gluing along curves. Similar techniques turn out to work in dimension 3 with spheres, but there are now many more shapes to cut along. Perhaps the nicest are the Haken manifolds, which contain a very nice surface one can repeatedly cut along. Not every 3-manifold is Haken, but it turns out every 3-manifold almost is: the surface can merely be twisted a finite number of times. The proof of this was a major milestone in 21st century mathematics. In the first of two talks discussing the proof of this result, we present an introduction to the classical theory at an introductory level. Intended for a general audience with some knowledge of algebraic topology.