 
Summary: arXiv:0812.5098v3[math.GT]18Aug2009
KNOTTING CORKS
SELMAN AKBULUT AND KOUICHI YASUI
Abstract. It is known that every exotic smooth structure on a simply con
nected closed 4manifold is determined by a codimention zero compact con
tractible 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 4manifolds such that they induce infinitely many different exotic
smooth structures. We also show that we can imbed an arbitrary finite num
ber of corks disjointly into 4manifolds, so that the corresponding involutions
on the boundary of the contractible 4manifolds give mutually different exotic
structures. Furthermore, we construct similar examples for plugs.
1. Introduction
In [1] the first author proved that E(2)#CP2 changes its diffeomorphism type if
we remove an imbedded copy of a Mazur manifold inside and reglue it by a natural
involution on its bounday. This was later generalized to E(n)#CP2 (n 2) by
BizacaGompf [8]. Here E(n) denotes the relatively minimal elliptic surface with
no multiple fibers and with Euler characteristic 12n. Recently, the authors [6]
and the first author [4] constructed many such examples for other 4manifolds.
The following general theorem was first proved independently by Matveyev [16],
