FRG: Holomorphic Curves in Low Dimensional Topology

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DMS-0244663Yakov 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 http://www.nsf.gov/pubs/2002/nsf02129/nsf02129.htmHolomorphic curves recently have emergedas a powerful tool in low-dimensional topology.The goal of this project is to unite and coordinateresearch in the area of applications of holomorphiccurves 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 SymplecticField Theory, is expected to provide a unified approachto many seemingly different problems in low-dimensionaltopologyThe impact of this project is expected to be much broaderthan its immediate goal of developing low-dimensionaltopology. There is a hope that the newly developed methodsopen new horizons in our understanding of linksbetween Topology and Theoretical Physics, and in particularString Theory. The project should also have a significanteducational value. In particular, under this project therewill be developed a Dissertation Subject Database,an actively managed and supported list of problems which willserve as a source of topics of PhD dissertation for graduatestudents of the senior project personnel.