Abstract: Sutured monopole Floer homology and sutured Instanton Floer homology were introduced by Kronheimer and Mrowka. They are tools to combines techniques from Gauge theory and the topology of 3-manifolds, and has many remarkable consequences, including a new proof of the Property P conjecture. Despite of those important applications, many basic aspects of the theory remains unclear: the functoriality, the gradings, and its relation with the Thurston norms, etc. In this talk, I will present some constructions and arguments which could resolve some of those mysteries.
