Fibrations, foliations and sutured manifolds

Geometry Topology Working Seminar
Friday, October 4, 2013 - 2:00pm
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
Gabai has a nice criteria for recognizing fibered knots in 3-manifolds. This criteria is best described in terms of sutured manifolds and simple sutured hierarchies. We will introduce this terminology and prove Gabai's result. Given time (or in subsequent talks) we might discuss generalizations concerning constructing foliations on knot compliments and 3-manifolds in general. Such results are very useful in understanding the minimal genus representatives of homology classes in the manifold (in particular, the minimal genus of a Seifert surface for a knot).