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.

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

References in corpus (4)

• Corks, Plugs and exotic structures
• Variations on Fintushel-Stern Knot Surgery on 4-manifolds
• Exotic rational elliptic surfaces without 1-handles
• The Dolgachev Surface

Cited by in corpus (7)

• Stable isotopy in four dimensions
• Topological quantum D-branes and wild embeddings from exotic smooth R^4
• Equivariant Corks
• Exotic smooth R^4 and certain configurations of NS and D branes in string theory
• Quantum D-branes and exotic smooth R^4
• Exotic R^4 and quantum field theory
• Group actions, corks and exotic smoothings of R^4