Contact conjecture for odd-dimensional moment-angle manifolds

Let $k=2m$ be even, let $\pmb{\Lambda}\subset\mathbb{R}^{2m}$ be an admissible configuration, and let $Z^{\mathbb{C}}(\pmb{\Lambda})$ be the associated odd-dimensional moment-angle manifold.

Contact conjecture for odd-dimensional moment-angle manifolds. For every admissible configuration $\pmb{\Lambda}\subset\mathbb{R}^{2m}$, the manifold $Z^{\mathbb{C}}(\pmb{\Lambda})$ is a contact manifold.

The conjecture proposes that all odd-dimensional moment-angle manifolds in this class admit contact structures. The paper gives examples and proves that these manifolds are almost contact and quasi-contact, but leaves the contact assertion open.