Khandhawit Tirasan



Stable homotopy invariants for 4-manifolds


    The Bauer-Furuta invariant can be considered as a stable homotopy refinement of the Seiberg-Witten invariant for a closed 4-manifold. Manolescu extended the idea to define a relative invariant for a 4-manifold with boundary. For an example, we can explicitly compute the Bauer-Furuta invariants for 4-manifolds (with or without boundary) possessing a metric of positive scalar curvature. The main technique is to deform the Seiberg-Witten map into its linearization.