Non-formal co-symplectic manifolds

TL;DR

This paper investigates the formality of mapping tori of manifolds, establishing conditions for non-formality via Massey products, and constructs explicit examples of non-formal co-symplectic manifolds in specific dimensions and Betti numbers.

Contribution

It provides new criteria for non-formality of mapping tori and constructs explicit examples of non-formal co-symplectic manifolds in certain dimensions and Betti number ranges.

Findings

Non-formal co-symplectic manifolds exist only in specific dimensions and Betti number configurations.

Conditions for non-zero Massey products in mapping tori are established.

Explicit examples of non-formal co-symplectic manifolds are constructed.

Abstract

We study the formality of the mapping torus of an orientation-preserving diffeomorphism of a manifold. In particular, we give conditions under which a mapping torus has a non-zero Massey product. As an application we prove that there are non-formal compact co-symplectic manifolds of dimension $m$ and with first Betti number $b$ if and only if $m=3$ and $b \geq 2$, or $m \geq 5$ and $b \geq 1$. Explicit examples for each one of these cases are given.