  7-dimensional closed and simply-connected manifolds have been attractive as
central and explicit objects in algebraic topology and differential topology of
higher dimensional closed and simply-connected manifolds, which were studied
actively especially in the 1950s--60s.
  Attractive studies of the class of these $7$-dimensional manifolds were
started by the discovery of so-called exotic spheres by Milnor. It has
influenced on the understanding of higher dimensional closed and
simply-connected manifolds via algebraic and abstract objects. Recently this
class is studied via more concrete notions from algebraic topology such as
concrete bordism theory by Crowley, Kreck, and so on.
  As a new kind of fundamental and important studies, the author has been
challenging understanding the class in constructive ways via construction of
fold maps, which are higher dimensional versions of Morse functions. The
present paper presents a new general method to construct ones on spin manifolds
of the class.

Algebraic Topology