Twisted stable homotopy type of Seiberg-Witten theory

Abstract: I will start by listing and discussing the important properties of a category, which I will denote C, of parametrized S1-equivariant spectra (I will try to make the talk comprehensible for an audience who may not be familiar with such categories). I will then discuss previous work constructing objects in C representing Seiberg-Witten theory, and exactly which assumptions are needed on the 3 manifolds to make this work. To upgrade this to a general 3 manifold, I will introduce the notion of a 1-cocycles in vector spaces, which describes twist so that one may extend C to include twisted objects. I will end by sketching how to use this in practice to generally construct a twisted stable homotopy type from Seiberg-Witten theory. This is joint work with Stefan Behrens and Alice Hedenlund.