  Closed (and simply-connected) manifolds whose dimensions are larger than 4
are central geometric objects in classical algebraic topology and differential
topology. They have been classified via algebraic and abstract objects. On the
other hand, It is difficult to understand them in geometric and constructive
ways.
  In the present paper, we show such studies via explicit fold maps, higher
dimensional versions of Morse functions. The author captured information of the
topologies and the differentiable structures of closed (and simply-connected)
manifolds which are not so complicated with respect to homotopy previously and
cohomology rings of more general closed (and simply-connected) manifolds via
construction of these maps. In the present paper, as a more precise work, we
capture so-called (triple) Massey products in this way.
