USask PIMS Geometry and Physics (GAP) Seminar: Gabe Islambouli

In 2016, Gay and Kirby showed that every compact smooth 4-manifold can be decomposed into three standard pieces. A particularly nice feature of this decomposition is that the smooth topology of the 4-manifold can be encoded by curves on a surface. In this talk, we explore the consequences of allowing more pieces in this decomposition, and show that many interesting cut and paste procedures can be carried out by natural mapping classes on the surface. We also explore a related decomposition for knotted surfaces in a 4-manifold.