Topology of Almost Complex Structures on Six-Manifolds

We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as sections twistor for a given metric. For connected six-manifold with vanishing first Betti number, we express quotient seven-sphere bundle over manifold by circle action, and then use this description to compute rational homotopy theoretic minimal model components that satisfy certain Chern number condition. further obtain formula homological intersection two in terms classes corresponding structures.