Non-trivial higher Massey products in moment-angle complexes

TL;DR

This paper introduces a unified method to construct non-trivial higher Massey products in the cohomology of moment-angle complexes, leading to new examples of non-formal manifolds across various geometric and algebraic fields.

Contribution

It provides a general combinatorial and homotopy-theoretic framework for constructing higher Massey products, extending all known examples in moment-angle complexes.

Findings

Constructed infinitely many non-formal manifolds.

Unified approach generalizes all existing Massey product examples.

Explicit methods for higher Massey products in topology and geometry.

Abstract

As part of various obstruction theories, non-trivial Massey products have been studied in symplectic and complex geometry, commutative algebra and topology for a long time. We introduce a general approach to constructing non-trivial Massey products in the cohomology of moment-angle complexes, using homotopy theoretical and combinatorial methods. Our approach sets a unifying way of constructing higher Massey products of arbitrary cohomological classes and generalises all existing examples of non-trivial Massey products in moment-angle complexes. As a result, we obtain explicit constructions of infinitely many non-formal manifolds that appear in topology, complex geometry and algebraic geometry.