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Special generic maps are higher dimensional versions of Morse functions withexactly two singular points, characterizing spheres topologically except4-dimensional cases and 4-dimensional standard spheres. The class of such mapsalso contains canonical projections of unit spheres.  This class is interesting from the viewpoint of algebraic topology anddifferential topology of manifolds. These maps have been shown to restrict thetopologies and the differentiable structures of the manifolds strongly byCalabi, Saeki and Sakuma before 2010s, and later Nishioka, Wrazidlo and theauthor. So-called exotic spheres admit no special generic map in considerablecases and homology groups and cohomology rings are shown to be stronglyrestricted. Moreover, special generic maps into Euclidean spaces whosedimensions are smaller than or equal to 4 have been studied well. The presentpaper mainly concerns cases where the dimensions of targets are greater than orequal to 5.

Notes on explicit special generic maps into Eulidean spaces whose dimensions are greater than 4