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ON THE TOPOLOGY OF COMPACT STEIN SURFACES SELMAN AKBULUT AND BURAK OZBAGCI
 

Summary: ON THE TOPOLOGY OF COMPACT STEIN SURFACES
SELMAN AKBULUT AND BURAK OZBAGCI
Abstract. In this paper we obtain the following results: (1) Any compact Stein
surface with boundary embeds naturally into a symplectic Lefschetz fibration over
S2
. (2) There exists a minimal elliptic fibration over D2
, which is not Stein. (3) The
circle bundle over a genus n 2 surface with euler number e = -1 admits at least
n + 1 mutually non-homeomorphic simply-connected Stein fillings. (4) Any surface
bundle over S1
, whose fiber is a closed surface of genus n 1 can be embedded into
a closed symplectic 4-manifold, splitting the symplectic 4-manifold into two pieces
both of which have positive b+
2 . (5) Every closed, oriented connected 3-manifold has
a weakly symplectically fillable double cover, branched along a 2-component link.
0. Introduction
In [AO] (see also [LP]), it was proved that every compact Stein surface admits a
PALF (positive allowable Lefschetz fibration over D2
with bounded regular fibers)
and conversely every PALF is Stein. In this paper we first prove that any compact

  

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

 

Collections: Mathematics