Stein 4-manifolds and corks

Details Stein 4-manifolds and corks Stein 4-manifolds and corks

2010-10-20

arxiv.org/abs/1010.4122v2

Mathematics

Geometric Topology

17 pages, 18 figures, minor corrections

Scientific paper

It is known that every compact Stein 4-manifolds can be embedded into a simply connected, minimal, closed, symplectic 4-manifold. Using this property, we give simple constructions of various cork structures of 4-manifolds. 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 (the authors previously gave examples of arbitrary many disjoint embeddings of different corks in a closed manifold inducing mutually different exotic structures). Furthermore, here we construct arbitrary many simply connected compact codimention zero submanifolds of S^4 which are mutually homeomorphic but not diffeomorphic.

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