Handle decompositions and smooth structures on 4-manifold

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The principal investigator studied smooth structures on 4-manifolds, using the diagrams of their handle decompositions. The main results are the following (1) - (3). The results (2) and (3) are joint works with Selman Akbulut (Michigan State University). (1) The principal investigator proved that a large class of 3-manifold bounds a 4-manifold which has infinitely many exotic smooth structures. (2) We gave a new sufficient condition under which a Gluck twist to a 4-manifold with odd intersection form does not change the smooth structure. (3) We constructed infinitely many simply connected Stein 4-manifolds with b2=2 that are mutually exotic. Moreover, they are Stein fillings of the same contact 3-manifold.