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

TL;DR

This paper explores the use of explicit fold maps to analyze the topology and differentiable structures of high-dimensional, simply-connected manifolds, focusing on capturing Massey products to understand their complex algebraic topology.

Contribution

It introduces a method to study high-dimensional manifolds through explicit fold maps, enabling the extraction of Massey products and topological information.

Findings

Captured topological and differentiable structure information using fold maps.

Provided a new approach to understanding Massey products in high-dimensional manifolds.

Enhanced the classification tools for simply-connected manifolds beyond traditional algebraic methods.

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.