  This article presents families of 7-dimensional closed and simply-connected
manifolds and fold maps on them such that squares of 2nd integral cohomology
classes may not be divisible by 2.
  Fold maps are higher dimensional versions of Morse functions. The author has
launched and been challenging the following new area: geometric and
constructive studies of higher dimensional, closed and simply-connected
manifolds. They are central objects in classical algebraic topology and
differential topology. They were classified via algebraic and abstract objects
in the last century and their understanding has been studied via concrete
algebraic topological theory such as concrete bordism theory since the
beginning of this century by Crowley, Kreck, Wang and so on.
  Fold maps are fundamental objects in the new area and the author has obtained
families of these manifolds and fold maps on the manifolds. The present paper
presents a new explicit result on the new area.
