English

Knotting corks

Geometric Topology 2014-02-26 v3

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.

Keywords

Cite

@article{arxiv.0812.5098,
  title  = {Knotting corks},
  author = {Selman Akbulut and Kouichi Yasui},
  journal= {arXiv preprint arXiv:0812.5098},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T11:56:41.274Z