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arXiv:0807.3815v2[math.GT]18Aug2009 SMALL EXOTIC STEIN MANIFOLDS
 

Summary: arXiv:0807.3815v2[math.GT]18Aug2009
SMALL EXOTIC STEIN MANIFOLDS
SELMAN AKBULUT AND KOUICHI YASUI
Abstract. It is known that the only Stein filling of the standard contact
structure on S3 is B4. In this paper, we construct pairs of homeomorphic but
not diffeomorphic simply connected compact Stein 4-manifolds, for any Betti
number b2 1; we do this by enlarging corks and plugs.
1. Introduction
A properly imbedded complex submanifold of an affine space X CN
is called a
Stein manifold. A compact smooth submanifold M X is called a Compact Stein
manifold if it is cut out from X by f c, where f : X R is a strictly pluri-
subharmonic (proper) Morse function, and c is a regular value. In particular M is
a symplectic manifold with convex boundary and the symplectic form = 1
2 f.
The form induces a contact structure on the boundary M. We call (M, ) a
Stein filling of the boundary contact manifold (M, ). Stein manifolds have been
a useful tools for studying exotic smooth structures on 4-manifolds, since smooth
4-manifolds can be decomposed into codimension zero Stein pieces (e.g [3], [5]).
In [8], [9] Eliashberg characterized the topology of Stein manifolds and proved

  

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

 

Collections: Mathematics