Subscribe to Events

Abstract: This talk will be an exposition on Seiberg-Witten equations on closed three manifolds; this is an abelian gauge theoretic equation that was introduced in the 90's. After suitable perturbations the moduli space of irreducible solutions to the Seiberg-Witten equations becomes zero dimensional manifold. The signed count of these solutions possibly with some counter term becomes a topological invariant of the three manifolds that is equal to either Milnor torsion or Casson-Walker invariant or Casson invariant. At the end we will also discuss non-abelian generalizations of these Seiberg-Witten equations and the prospect of defining invariants.