11 problems

Battaglia–Zaffran's conjectures. The basic cohomology ring $H^{*}_{\mathcal{F}_{\mathfrak h}}(\mathcal{Z}_{\mathcal{K}})$ should have a description similar to the cohomology ring o…

Let $\mathcal{K}$ be a three-dimensional simplicial sphere, and let $\mathcal{Z}_{\mathcal{K}}$ be its moment-angle manifold. Suppose that either $\mathcal{K}^1$ is a chordal graph…

Spherical orbit-space conjecture. The space $N(P,\lambda)$ is homeomorphic to $S^n$ if and only if

Let $M_{\boldsymbol{bbLambda}}$ be a moment-angle manifold associated with a simple polytope, and let the dual polytope be neighborly. Bosio–Meersseman's conjecture. The manifold…

Contact-structure conjecture. Every odd-dimensional moment-angle manifold admits a contact structure.

Diffeomorphism conjecture. $\mathcal{Z}_{K}$ is diffeomorphic to the connected sum of sphere products in Proposition 1.

Gitler–López conjecture. $Z_v$ is diffeomorphic to

Contact conjecture for odd-dimensional moment-angle manifolds. For every admissible configuration $\pmb{\Lambda}\subset\mathbb{R}^{2m}$, the manifold…

Martínez–Muñoz–Presas conjecture. Every almost contact manifold is in fact a contact manifold.

Let $P$ be a simple polytope, meaning that exactly $\operatorname{dim}(P)$ facets meet at each vertex. A simple polytope is realized as a face of another polytope when it is combin…

Let $P$ be a simple polytope and let $Z^{\mathbf C}$ denote its associated complex moment-angle manifold. A polytope is dual-neighborly when every collection of at most $[d/2]$ fac…