Department Seminars & Colloquia
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Since the inception of Donaldson theory and Seiberg-Witten theory in late 20 century, the invariants induced from these gauge theories, in particular, Seiberg-Witten invariants have become so powerful tools in study of smooth and symplectic 4-manifolds. Nevertheless, it has not been much known that one can distinguish smooth and symplectic 4-manifolds to some extent using Seiberg-Witten invariants.
In this talk I'd like to show that there exist an infinite family of non-simply connected, non-diffeomorphic, but homeomorphic, 4-manifolds with the same Seiberg-Witten invariants. The main techniques used in the construction are a knot surgery technique and a covering method.