1998/11/15 by Terry Fuller, Fuller, Terry
Mathematics · #57M12 (Secondary) #57R55 (Primary) #57R65 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:57M12 #msc:57R55 #msc:57R65
paper · pdf · doi:10.48550/arxiv.math/9811093
22 pages, 18 figures; main theorems changed from earlier version
arxiv created 1999/03/25 · arxiv updated 2009/11/30
Let M be a smooth 4-manifold which admits a relatively minimal hyperelliptic genus h Lefschetz fibration over the 2-sphere. If all of the vanishing cycles for this fibration are nonseparating curves, then we show that M is a 2-fold cover of a 2-sphere bundle over the 2-sphere, branched over an embedded surface. If the collection of vanishing cycles for this fibration includes separating curves, we show that M is the relative minimalization of a Lefshetz fibration N, with N a 2-fold branched cover of a rational surface, branched over an embedded surface.