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Proceedings of 5th Geometry-Topology Conference,

Summary: Proceedings of 5th
Geometry-Topology 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 4-manifolds 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
(1-handles) (2-handles) be four-dimensional han-
dlebody with one 0-handle and no 3- or 4-handles. Then
· The standard PC-structure on B4
can be extended over 1-handles so that manifold
X1 = B4
(1-handles) has pseudo-convex boundary.
· If each 2-handle is attached to X1 along a Legendrian knot with framing one less
then Thurston-Bennequin framing of this knot then the symplectic form on X1 can be


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


Collections: Mathematics