Abstract
This is a survey of our recent work with Tom Mrowka on Seiberg-Witten gauge theory and index theory for manifolds with periodic ends. We explain how this work leads to a new invariant, which is related to the classical Rohlin invariant of homology 3-spheres and to the Furuta-Ohta invariant originating in Yang-Mills gauge theory. We give some new calculations of our invariant for 4-dimensional mapping tori.
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