Yakov Eliashberg, John Etnyre, Wu-Chung Hsiang, Michael Hutchings, Tomasz Mrowka, Peter Ozsvath, Ronald Stern, Zoltan Szabo.
This is a Division of Mathematical Sciences Focused Research Group (FRG) award made under solicitation www.nsf.gov/pubs/2002/nsf02129/nsf02129.htm
Holomorphic curves recently have emerged as a powerful tool in low-dimensional topology. The goal of this project is to unite and coordinate research in the area of applications of holomorphic curves in order to: - construct new invariants of manifolds of dimension 3 and 4; - develop new methods for proving diffeomorphism between the manifolds; - find new relations between string theory and symplectic geometry on the one side, and knot theory and topology of 3-manifolds on the other. The core of this project, Embedded Symplectic Field Theory, is expected to provide a unified approach to many seemingly different problems in low-dimensional topology
The impact of this project is expected to be much broader than its immediate goal of developing low-dimensional topology. There is a hope that the newly developed methods open new horizons in our understanding of links between Topology and Theoretical Physics, and in particular String Theory. The project should also have a significant educational value. In particular, under this project there will be developed a Dissertation Subject Database, an actively managed and supported list of problems which will serve as a source of topics of PhD dissertation for graduate students of the senior project personnel.