Naturality in sutured monopole homology

Naturality in sutured monopole homology

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Steven Sivek , Princeton University
Fine Hall 314

Kronheimer and Mrowka defined a version of monopole Floer homology which assigns to any balanced sutured manifold a module up to isomorphism. In this talk, I will discuss how to replace “a module up to isomorphism” with something more natural, by showing that different choices made in the construction are related by canonical isomorphisms which are well-defined up to multiplication by a unit. This allows us to construct some interesting functors out of sutured monopole homology and to talk about elements of it, and I will outline some applications of this fact to contact geometry. This is joint work with John Baldwin.