Knotting corks

Details Knotting corks Knotting corks

2008-12-30

arxiv.org/abs/0812.5098v3

Mathematics

Geometric Topology

19 pages, 20 figures, the second author's address is changed, revised version, to appear in Journal of Topology

Scientific paper

It is known that every exotic smooth structure on a simply connected closed 4-manifold is determined by a codimention zero compact contractible Stein submanifold and an involution on its boundary. Such a pair is called a cork. In this paper, we construct infinitely many knotted imbeddings of corks in 4-manifolds such that they induce infinitely many different exotic smooth structures. We also show that we can imbed an arbitrary finite number of corks disjointly into 4-manifolds, so that the corresponding involutions on the boundary of the contractible 4-manifolds give mutually different exotic structures. Furthermore, we construct similar examples for plugs.

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