Obstruction theory and coincidences in positive codimension

Let f, g : X → Y be two maps between closed manifolds with dim X ≥ dim Y = n ≥ 3. We study the primary obstruction o n (f, g) to deforming f and g to be coincidence free on the n–th skeleton of X. We give examples for which obstructions to deforming f and g to be coincidence free are detected by o n (f, g).