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Nonexistence of twists and surgeries generating exotic 4-manifolds

Hold Date
2018-05-11 16:00〜2018-05-11 17:00
Lecture Room S W1-C-514, West Zone 1, Ito campus, Kyushu University
Object person
Kouichi YASUI (Osaka University)

In dimension four, there are still no manifolds whose all (exotic) smooth structures are found. On the other hand, it is well known that, under a certain condition, infinitely many exotic smooth structures on a 4-manifold are generated by twisting (a neighborhood of) an embedded torus. Thus it would be natural to ask whether a (simply connected closed) 4-manifold admits a submanifold such that all exotic smooth structures are generated by twisting the submanifold. In this talk, we give a partial negative answer to this problem, and moreover, we give similar results for more general surgeries.