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.

arXiv comment14 pages, incorrect stuffs are due to my carelessness, this is submitted to another (refereed) journal

References in corpus (5)

• Standard Special Generic Maps of Homotopy Spheres into Euclidean Spaces
• Notes on fold maps obtained by surgery operations and algebraic information of their Reeb spaces
• On the classification of 1-connected 7-manifolds with torsion free second homology
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Cited by in corpus (5)

• Closed manifolds admitting no special generic maps whose codimensions are negative and their cohomology rings
• Notes on explicit special generic maps into Eulidean spaces whose dimensions are greater than 4
• Global topologies of Reeb spaces of stable fold maps with non-trivial top homology groups
• The topologies and the differentiable structures of the images of special generic maps having simple structures
• A differential topological study of compact manifolds having simple structures