URegina Topology Seminar: Martin Frankland

The classification of 2-dimensional TQFTs was obtained by cutting up surfaces into disks, cylinders, and pairs of pants. In higher dimension, such a decomposition of n-manifolds is not available. We need to cut up manifolds not only along codimension 1 submanifolds, but also strata of codimension 2 or higher. Those refined cutting rules lead to the notion of an extended TQFT. I will sketch some attempts at making this notion precise, and how the data can be described using higher categories.