Twisted Manolescu-Floer Spectra for Seiberg-Witten Monopoles

In this thesis, we extend Manolescus and Kronheimer-Manolescus construction of Floer homotopy type to general 3-manifolds. This Floer homotopy type is a candidate for an object whose suitable homology groups recover Floer homology. The main idea is to apply finite dimensional approximation technique and Conley index theory to Seiberg-Witten theory of 3-manifolds. Another part of the construction involves a concept of twisted parametrized spectra introduced by Douglas. We also provide explicit computation for the manifolds S¹ × S² and T³. (Copies available exclusively from MIT Libraries, libraries.mit.edu/docs - [email protected])