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

Special generic maps and fold maps and information on triple Massey products of higher dimensional differentiable manifolds