 
Summary: CORK TWISTING EXOTIC STEIN 4MANIFOLDS
SELMAN AKBULUT AND KOUICHI YASUI
Abstract. From any 4dimensional oriented handlebody X without 3 and
4handles and with b2 1, we construct arbitrary many compact Stein 4
manifolds which are mutually homeomorphic but not diffeomorphic to each
other, so that their topological invariants (their fundamental groups, homol
ogy groups, boundary homology groups, and intersection forms) coincide with
those of X. We also discuss the induced contact structures on their boundaries.
Furthermore, for any smooth 4manifold pair (Z, Y ) such that the complement
Z  int Y is a handlebody without 3 and 4handles and with b2 1, we con
struct arbitrary many exotic embeddings of a compact 4manifold Y into Z,
such that Y has the same topological invariants as Y .
1. Introduction
A basic problem of 4manifold topology is to find all exotic copies of smooth
4manifolds, in particular to find various methods of constructing different smooth
structures on 4manifolds (e.g. logarithmic transform [12], FintushelStern's rational
blowdown [16] and knot surgery [17]). The purpose of this paper is to approach
this problem by corks and give applications. Since different smooth structures on a
4manifold can be explained by existence corks which divide the manifold into two
Stein pieces [4], cork twisting Stein manifolds is a central theme of this paper.
