 
Summary: Proceedings of 5th
GĻokova
GeometryTopology Conference,
pp, .
Exotic structures and adjunction inequality
Selman Akbulut and Rostislav Matveyev
1. Introduction
Here we want to discuss easy "natural" proofs of the some old difficult theorems of 4
manifolds by the aid of recently proven modern tools. One of the important recent results
of smooth 4manifolds is Eliashberg's topological description of compact Stein manifolds,
that is symplectic manifolds with pseudoconvex boundary (PC  manifolds):
Theorem 1.1. ([E]) Let X = B4
(1handles) (2handles) be fourdimensional han
dlebody with one 0handle and no 3 or 4handles. Then
· The standard PCstructure on B4
can be extended over 1handles so that manifold
X1 = B4
(1handles) has pseudoconvex boundary.
· If each 2handle is attached to X1 along a Legendrian knot with framing one less
then ThurstonBennequin framing of this knot then the symplectic form on X1 can be
