Speaker
Shawn Cui, Purdue University
AbstractTopological quantum field theories (TQFTs) provide quantum invariants that are useful to distinguish manifolds. In dimension 4, it is known that semisimple TQFTs cannot detect smooth structures of manifolds. We develop a framework to construct quantum invariants of 4-manifolds that can potentially extend to the nonsemisimple setting. The resulting invariants reduce to the Crane-Yetter invariants in special cases. We also provide extensions to include cohomology data of 4-manfolds in the construction.