Gauge Theory and Low Dimensional Topology

Princeton University, Princeton NJ

Investigators

Abstract

The main theme of this project is the study of knots, three dimensional manifolds and smooth 4-manifolds by using Heegaard Floer homology, gauge theory and symplectic geometry. Potential applications would include the construction of new invariants for knots and links, better understanding of those knots that admit lens space surgeries and and the construction of new exotic smooth structures on 4-manifolds. The PI also proposes to study the structure of the Floer homology invariants and their relationship with smooth 4-manifold invariants. The proposal studies the relationship between Seiberg-Witten and Heegaard Floer homologies and their applications. While the latter theory uses topological tools and symplectic geometry, the former uses the Seiberg-Witten equations that are related to gauge theory and mathematical physics. Progress in this direction should lead to a better understanding of connections between low dimensional topology and gauge theory.