Morse functions on surfaces, the pants complex, and 4-manifolds

Geometry Topology Seminar Pre-talk
Monday, December 5, 2022 - 12:45pm for 1 hour (actually 50 minutes)
Skiles 006
Gabriel Islambouli – UC Davis
Austin Christian

We show how to obtain a decomposition of an arbitrary closed, smooth, orientable 4-manifold from a loop of Morse functions on a surface or as a loop in the pants complex. A nice feature of all of these decompositions is that they can be encoded on a surface so that, in principle, 4-manifold topology can be reduced to surface topology. There is a good amount to be learned from translating between the world of Morse functions and the world of pants decompositions.  We will allude to some of the applications of this translation and point the interested researcher to where they can learn more. No prior knowledge of these fields is assumed and there will be plenty of time for questions.