Geometric Group Therapy Seminar

Speaker: Xiaozhou Zhou

Title: Decompositions of smooth manifolds

Abstract:

A Heegaard splitting decomposes a closed orientable 3-manifold into two handlebodies glued along a common surface. This gives a way to encode a 3-manifold by lower-dimensional data on a surface. In dimension four, the analogous is a trisection, introduced by Gay and Kirby, in which a smooth 4-manifold is decomposed into three 4-dimensional handlebodies with controlled intersections.

In this talk, I will start with basic examples of Heegaard splittings, their diagrams, and stabilization, and then explain how these ideas extend to trisections of 4-manifolds. Finally, I will briefly discuss multisections in higher dimensions. This will be an introductory talk, with an emphasis on the geometric ideas behind these decompositions.