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arXiv:0812.5098v3[math.GT]18Aug2009 KNOTTING CORKS
 

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 4-manifold 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 4-manifolds 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 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.
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
Bizaca-Gompf [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 4-manifolds.
The following general theorem was first proved independently by Matveyev [16],

  

Source: Akbulut, Selman - Department of Mathematics, Michigan State University

 

Collections: Mathematics