Maps on 3-manifolds given by surgery
  Suppose that the 3-manifold M is given by integral surgery along a link L in S^3. In the following we construct a stable map from M to the plane, whose singular set is canonically oriented. We obtain upper bounds for the minimal numbers of crossings and non-simple singularities and of connected components of fibers of stable maps from M to the plane in terms of properties of L. 
Boldizsar Kalmar, Andras I. Stipsicz
math.GT