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Journal of Gokova Geometry Topology Volume 2 (2008) 4082

Summary: Journal of GĻokova Geometry Topology
Volume 2 (2008) 40­82
Corks, Plugs and exotic structures
Selman Akbulut and Kouichi Yasui
Abstract. We discuss corks, and introduce new objects which we call plugs. Though
plugs are fundamentally different objects, they also detect exotic smooth structures
in 4-manifolds like corks. We discuss relation between corks, plugs and rational blow-
downs. We show how to detect corks and plugs inside of some exotic manifolds.
Furthermore, we construct knotted corks and plugs.
1. Introduction
Let Wn, Wn and Wm,n be the smooth 4-manifolds given by Figure 1. Notice that W1
is a version of the manifold defined in [22] by Mazur, and Wn is the "positron" intro-
duced by the first author and Matveyev [8]. The first author [1] proved that E(2)#CP
changes its diffeomorphism type by regluing an imbedded copy of W1 inside via a natu-
ral involution on the boundary W1. This was later generalized to E(n)#CP
(n 2)
by Bizaca-Gompf [11]. The following general theorem was first proved independently by
Matveyev [21], Curtis-Freedman-Hsiang-Stong [13], and later on strengthened by the first


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


Collections: Mathematics