An exact manifold with pseudoconvex boundary (PC manifold, for short) is a compact complex manifold X, which admits a strictly pluri-subharmonic Morse function Ïˆ, such that the set of maximum pointsâ€¦ (More)

Nutzungsbedingungen Mit dem Zugriff auf den vorliegenden Inhalt gelten die Nutzungsbedingungen als akzeptiert. Die angebotenen Dokumente stehen fÃ¼r nicht-kommerzielle Zwecke in Lehre, Forschung undâ€¦ (More)

Theorem 1.1. ([E]) Let X = B âˆª (1-handles) âˆª (2-handles) be four-dimensional handlebody with one 0-handle and no 3or 4-handles. Then â€¢ The standard symplectic structure on B can be extended overâ€¦ (More)

Here we construct a fake smooth structure on a compact contractible 4-manifold W , where W is a well-known Mazur manifold obtained by attaching in two-handle to S x B along its boundary as in Figureâ€¦ (More)

We discuss corks, and introduce new objects which we call plugs. Though plugs are fundamentally different objects, they also detect exotic smooth structures in 4-manifolds like corks. We discussâ€¦ (More)

We show that the infinite sequence of homotopy 4spheres constructed by Cappell-Shaneson are all diffeomorphic to S. This generalizes previous results of Akbulut-Kirby and Gompf. 0. Introductionâ€¦ (More)

Here we show that every compact smooth 4-manifold X has a structure of a Broken Lefschetz Fibration (BLF in short). Furthermore, if b 2 (X) > 0 then it also has a Broken Lefschetz Pencil structureâ€¦ (More)

Here we study the deformations of associative submanifolds inside a G 2 manifold M 7 with a calibration 3-form Ï•. A choice of 2-plane field Î› on M (which always exits) splits the tangent bundle of Mâ€¦ (More)

We show that there exist infinitely many simply connected compact Stein 4-manifolds with b2 = 2 such that they are all homeomorhic but mutually non-diffeomorphic, and they are Stein fillings of theâ€¦ (More)