Monopole Floer homology for 3-manifolds with torus boundary

Monopole Floer homology for 3-manifolds with torus boundary

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Donghao Wang, Massachusetts Institute of Technology

Zoom link:  https://princeton.zoom.us/j/453512481

 

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 boundary, whose Euler characteristic recovers the Milnor-Turaev torsion invariant by a classical theorem of Meng-Taubes. It also satisfies a (3+1) TQFT property. In the end, we will explain its relation with gauged Landau-Ginzburg models and point out some future directions.