Principal Investigator: Selman Akbulut
Abstract: The principal investigator will investigate the topology of smooth 4-manifolds. By decomposing smooth manifolds into complex pieces, he will use the techniques of complex and symplectic manifolds to understand the restriction this decomposition imposes on the topology of smooth 4-manifolds. The principal investigator hopes to apply the techniques from the solution of the `Scharlemann problem' and Fintushel-Stern constructions to the problem of constructing 4-dimensional fake s-cobordisms, and to the problem of constructing a fake copy of `three-sphere crossed with circle'. He would like to study topology of Horikawa surfaces and hopes to give affirmative answers to various branched covering conjectures.
The principal investigator intends to study generalized 4-dimensional spaces (4-manifolds); he hopes to find new ones. These spaces arise naturally in physics: relativity (space-time) and quantum field theories. Recently there have been exciting developments about the structure of these spaces coming from the ideas of physics, but we still don't know if certain basic exotic 4-manifolds could exist. If they exist they will be basic building blocks of the known ones. We would like to investigate possible constructions which could give their existence.
