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

Abstract: 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.