Floer Homology for three manifolds and its applications

Abstract

Floer homology theories for 3-manifolds come from many sources Instantons, Seiberg-Witten Monopoles,  Heegaard Floer and Embedded Contact Floer theories.  They have proven to be a powerful tools in low dimensional topology. I’ll try to outline some of their applications and give some prospects for some future directions.  This is meant to be a fly over without (m)any details hopefully accessible to a rather general mathematics audience.