Floer theory and its topological applications (Q256552)

This paper is an exposition of several flavors of Floer homology for 3-manifolds together with a review of some applications. In particular, Manolescu gives overviews of Instanton homology, the Atiyah-Floer suggestion of Lagranginan Floer theory in the moduli of flat connections associated to a Heegaard splitting, Monopole Floer homology, Heegaard Floer theory and Floer stable homotopy theory. This paper was written based on a series of lectures the author gave in Japan shortly after completing the answer to the triangulation question for manifolds. The paper is easy to follow and contains ample references to the literature for people wishing to learn more.