Published in Journal of Gökova Geometry Topology, Volume 6 (2012)
Title Stein 4-manifolds and corks
Author Selman Akbulut and Kouichi Yasui
It is known that every compact Stein 4-manifolds can be embedded into a simply connected, minimal, closed, symplectic 4-manifold. By using this property, we discuss a new method of constructing corks. This method generates a large class of new corks including all the previously known ones. We prove that every one of these corks can knot in infinitely many different ways in a closed smooth manifold, by showing that cork twisting along them gives different exotic smooth structures. We also give an example of infinitely many disjoint embeddings of a fixed cork into a non-compact 4-manifold which produce infinitely many exotic smooth structures. Furthermore, we construct arbitrary many simply connected compact codimension zero submanifolds of S4 which are mutually homeomorphic but not diffeomorphic.
Keywords Stein 4-manifold, cork, plug, knot surgery, rational blowdown
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Submitted: Oct 27, 2012
Accepted: Dec 29, 2012
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