Minimizing coincidence in positive codimension

Let f and g be maps between smooth manifolds M and N of dimensions n + m and n, respectively (where m > 0 and n > 2). Suppose that the image (fxg)(M) intersects the diagonal N × N in finitely many points, whose preimages are smooth m-submanifolds inM. The problem of minimizing the coincidence set Coin(f, g) of the maps f and g with respect to these preimages and/or their components is considered. The author’s earlier results are strengthened. Namely, sufficient conditions under which such a coincidence m-submanifold can be removed without additional dimensional constraints are obtained.