  Special generic maps are higher dimensional versions of Morse functions with
exactly two singular points, characterizing spheres topologically except
4-dimensional cases and 4-dimensional standard spheres. The class of such maps
also contains canonical projections of unit spheres.
  This class is interesting from the viewpoint of algebraic topology and
differential topology of manifolds. These maps have been shown to restrict the
topologies and the differentiable structures of the manifolds strongly by
Calabi, Saeki and Sakuma before 2010s, and later Nishioka, Wrazidlo and the
author. So-called exotic spheres admit no special generic map in considerable
cases and homology groups and cohomology rings are shown to be strongly
restricted. Moreover, special generic maps into Euclidean spaces whose
dimensions are smaller than or equal to 4 have been studied well. The present
paper mainly concerns cases where the dimensions of targets are greater than or
equal to 5.
