Topology of Asymptotically Conical Calabi–Yau and G2 Manifolds and Desingularization of Nearly Kähler and Nearly G2 Conifolds

Abstract A natural approach to the construction of nearly $$G_2$$ G 2 manifolds lies in resolving spaces with isolated conical singularities by gluing asymptotically modelled on same cone. If such a resolution exits, one expects there be family manifolds, whose endpoint is original conifold and parameter scale glued manifold. We show that many cases curve does not exist. The non-existence result based topological for manifolds: if rate metric below $$-3$$ - 3 , then 4-form exact only manifold Euclidean $$\mathbb R^7$$ R 7 . similar possible Kähler case, which we investigate manner results. In this results Calabi–Yau 6-manifolds: square form complex volume can simultaneously exact, R^6$$ 6