4 problems

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Conjecture on the emptiness of the classes $\mathcal{Z}_1$ and $\mathcal{Z}_4$
Emptiness conjecture. The classes $\mathcal{Z}_1$ and $\mathcal{Z}_4$ are both empty.
Conjectureopenalmost-hermitian-geometry differential-geometry nilmanifoldsarXiv posted 2 days ago
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Classification conjecture for compact non-Kähler almost Hermitian 4-manifolds of class $\mathcal{AH}_1$
Classification conjecture. If $(M^4,g,J,\omega)$ is a compact 4-dimensional almost Hermitian manifold of class $\mathcal{AH}_1$ , then either the manifold is Kähler, or it is one of…
Conjectureopenalmost-hermitian-geometry four-manifoldsarXiv posted 2 days ago
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Conjecture on Gray–Hervella classes of almost Hermitian structures on the Iwasawa manifold
Iwasawa manifold Gray–Hervella conjecture. The manifold $\undertilde{\mathcal{M}}$ cannot admit almost Hermitian structures in the classes $\mathcal{W}_1$ and $\mathcal{W}_4$ .
Conjectureopenalmost-hermitian-geometry gray-hervella-classes iwasawa-manifoldarXiv posted 2 days ago
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Almost-Hermitian structure conjecture for moduli spaces of non-Abelian monopoles and projective vortices
Let the base be a four-manifold of Seiberg–Witten simple type, and consider moduli spaces of non-Abelian monopoles and, more generally, projective vortices associated with suitably…
Conjectureopenalmost-hermitian-geometry gauge-theory moduli-spacesarXiv posted 2 days ago

Conjecture on the emptiness of the classes Z1\mathcal{Z}_1Z1​ and Z4\mathcal{Z}_4Z4​