Student 3-Manifold Seminar: Haken hierarchies

Seminar | April 5 | 4:10-5:30 p.m. | 939 Evans Hall

 Michael Klug, UC Berkeley

 Department of Mathematics

Compact surfaces with non-positive Euler characteristic can be inductively decomposed by cutting along finitely many properly embedded loops and arcs until one is left with a collection of disks; such a decomposition is called a hierarchy. An analogue up a dimension is called a Haken manifold, which can be inductively decomposed by cutting along two-sided incompressible surfaces until one is left with a collection of balls. Examples of Haken manifolds include link complements and surface bundles over circles. Certain facts about Haken manifolds can be proved by induction on a hierarchy.

 kmill@berkeley.edu