Geometry & Topology Seminar

Gabriel Islambouli, Deaprtment of Pure Mathematics, University of Waterloo

"Smooth 4-manifolds and the Pants Complex"

We show how objects typically used to study surfaces can be used to give insights into the structure of smooth 4-manifolds. In particular, we construct a correspondence between loops in the pants complex and smooth, closed, oriented 4-manifolds. We use this correspondence, together with the fact that the pants complex is simply connected, to show that the cobordism group of such 4-manifolds is isomorphic to the integers. We also discuss how this correspondence can be used to give insights into the structure of the pants complex.

MC 5403