Knotting corks
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.
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