7 problems

An exotic $\mathbb{R}^{4}$ is a smooth 4-manifold homeomorphic but not diffeomorphic to the standard $\mathbb{R}^{4}$. The handlebody construction gives such an exotic smooth struc…

In the setting of exotic smoothness described above, naked singularities arise in non-canceling handle pairs, while the same exotic smoothness is associated with particles. Geometr…

Let $M$ be a smooth 4-manifold equipped with an exotic smoothness structure $M_K$ constructed by knot surgery. The construction decomposes the associated contributions into a knott…

In a 4-dimensional h-cobordism between 3-manifolds, non-canceling pairs of 2-handles give rise to naked singularities, while exotic smoothness is associated with physically interpr…

Knot-and-link generation conjecture. All distinct exotic smoothness structures of the compact 4-manifold $M=E(2)$ can be generated by knots and links.

Let $M$ be a 4-manifold, either compact or non-compact, equipped with an exotic smooth structure. An external gravitational source is a contribution to the gravitational field aris…

Let $S^{3}$ be a 3-sphere admitting a codimension-1 foliation with integer Godbillon–Vey invariant. An exotic 4-disk is a smooth 4-disk whose smooth structure is exotic. Exotic 4-d…