2010/10/20 by Selman Akbulut, Akbulut, Selman, Kouichi Yasui +1
Mathematics · #57R55 #57R65 #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:57R55 #msc:57R65
paper · pdf · doi:10.48550/arxiv.1010.4122
19 pages, 18 figures, minor changes. arXiv admin note: text overlap with arXiv:0812.5098
openalex publication_date 2010/10/20 · arxiv created 2012/10/31 · arxiv updated 2012/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.