Massey products in cohomology of moment-angle manifolds corresponding to Pogorelov polytopes

TL;DR

This paper constructs nontrivial Massey products in the cohomology of moment-angle manifolds associated with Pogorelov polytopes, revealing their nonformality and advancing understanding of their topological complexity.

Contribution

It introduces the first explicit construction of nontrivial Massey products for moment-angle manifolds linked to Pogorelov polytopes, including fullerenes.

Findings

Existence of nontrivial Massey products in these manifolds

Nonformality of the corresponding spaces

Extension to polytopes like the dodecahedron and fullerenes

Abstract

In this work we construct nontrivial Massey products in the cohomology of moment-angle manifolds corresponding to polytopes from the Pogorelov class. This class includes the dodecahedron and all fullerenes, i. e. simple 3-polytopes with only 5-gonal and 6-gonal facets. The existence of a nontrivial Massey product implies the nonformality of the space in the sense of rational homotopy theory.