Knotting corks

Selman Akbulut; Kouichi Yasui

doi:10.1112/jtopol/jtp025

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arXiv · 0812.5098

Knotting corks

Selman Akbulut·Kouichi Yasui

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Abstract

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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Selman Akbulut, Kouichi Yasui. 2009-08-18. Knotting corks. https://doi.org/10.1112/jtopol%2Fjtp025

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