Monopole Floer homology for 3-manifolds with torus boundary
The monopole Floer homology of an oriented closed 3-manifold was defined by Kronheimer-Mrowka around 2007 and has greatly influenced the study of 3-manifold topology since its inception.
In this talk, we will generalize their construction and define the monopole Floer homology for any oriented 3-manifolds with torus bound- ary, whose Euler charateristic recovers the Milnor-Turaev torsion in- variant by a classical theorem of Meng-Taubes. It also satisfies a (3+1) TQFT property. We will talk a little bit about the analytic aspect of this construction and explain its relation with gauged Landau-Ginzburg models.