UCLA

In this thesis, we define different versions of unfolded Seiberg-Witten Floer spectra for general 3-manifolds. They generalize Manolescu's and Kronheimer-Manolescu's construction of Floer stable homotopy type. We prove some properties of these new invariants and give some topological applications (Joint works with collaborators.) Along the way, as an application of the Seiberg-Witten Floer spectrum, we study the Pin(2)-equivariant Seiberg-Witten Floer KO-theory and prove new Furuta-type inequalities on the intersection forms of spin cobordisms between homology 3-spheres.