4 problems

Let $\Phi_t$ be a one-parameter family of moduli-spaces arising from a one-parameter family of structures on the ambient manifold, where $\Phi_0$ compactifies to a fibration of tha…

A compact 7-manifold with holonomy $G_2$ is a Riemannian 7-manifold whose holonomy group is $G_2$. A coassociative submanifold is a four-dimensional calibrated submanifold in a…

A TCS $G_2$ manifold $X$ is constructed by gluing asymptotically cylindrical Calabi–Yau three-folds, and globally it can be viewed as a $K3$ fibration over $S^3$: … The fiber is a…

Let $M$ be the compact $G_2$ manifold under consideration, and let the associatives $\tilde{C}_\gamma$ be the three-spheres obtained from $S^1_{x_3}$ and sections of the relevant e…