On the topology of compact Stein surfaces
Abstract
In this paper we obtain the following results: (1) Any compact Stein surface with boundary embeds naturally into a symplectic Lefschetz fibration over the 2sphere. (2) There exists a minimal elliptic fibration over the 2disk, which is not Stein. (3) The circle bundle over a genus n>1 surface with euler number e=1 admits at least n+1 mutually nonhomeomorphic simplyconnected Stein fillings. (4) Any surface bundle over the circle, whose fiber is a closed surface of genus n>0 can be embedded into a closed symplectic 4manifold, splitting the symplectic 4manifold into two pieces both of which have positive b_2^+. (5) Every closed, oriented connected 3manifold has a weakly symplectically fillable double cover, branched along a 2component link.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:math/0103106
 Bibcode:
 2001math......3106A
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Algebraic Geometry;
 57R55;
 57M99
 EPrint:
 14 pages, 10 figures