A sharp lower bound is established on the self-intersections of fold singularities for stable maps from oriented surfaces to R^2 by reducing the problem to bounds on immersed surface boundaries.
Simple stable maps of 3-manifolds into surfaces.Topology, 35(3):671–698, Jul 1996
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A Lower Bound on the Self-intersections of Fold Singularities
A sharp lower bound is established on the self-intersections of fold singularities for stable maps from oriented surfaces to R^2 by reducing the problem to bounds on immersed surface boundaries.