Georgia Institute of Technology College of Sciences

The topic of smooth 4-manifolds is a long established, yetunderdeveloped one. Its mystery lies partly in its wealth of strangeexamples, coupled with a lack of generally applicable tools to putthose examples into a sensible framework, or to effectively study4-manifolds that do not satisfy rather strict criteria. I will outlinerecent work that associates objects from symplectic topology, calledweak Floer A-infinity algebras, to general smooth, closed oriented4-manifolds. As time permits, I will speculate on a "genus-g Fukayacategory of smooth 4-manifolds.