11 problems

Canonical basic class conjecture. Any manifold obtained this way should have the canonical class, up to sign, as its only Seiberg–Witten basic class.

Exotic tori carry no symplectic structures. There are no symplectic structures on exotic tori.

Let $Z_1$ denote the quotient of $S^2\times S^2$ by the fixed-point-free involution that applies the antipodal map to both $S^2$ factors. For the manifolds and values of $l$ descri…

Let $BK$ be the symplectic four-manifold constructed in the paper, and let $V_n$ be the sequence of exotic four-manifolds obtained from $BK$, with $V_1=BK$. For a smooth four-manif…

Let $AP$ be the four-manifold constructed in the paper, and let $Z_n$ be the infinite family of exotic four-manifolds obtained by replacing the final Luttinger surgery with torus s…

An exotic $R^4$ is a smooth manifold homeomorphic but not diffeomorphic to the standard $\mathbf{R}^4$. Centrality conjecture. This exotic $R^4$ is central for understanding both t…

Monopole-moduli gravitational-instanton conjecture. Precisely ${\cal M}_{2}^{0}$, being the gravitational instanton, gives the dominant contribution to the Euclidean path integral…

Let a fixed radial family of exotic smooth structures on $\mathbb{R}^4$ be embedded in a local CalabiYau threefold, and let $E_2$ denote the propagator of the KodairaSpencer theory…

Let $Y_{2m}$ and $Z_{2m}$ denote the manifolds obtained from $Y$ and $Z$, respectively, by generalized cork twists of exponent $2m$. Infinite exotic structures conjecture. The fami…

Akbulut's cork conjecture. It might be possible to choose $A$ so that

A small exotic smooth $\mathbb{R}^{4}$ is related to a factor $III$ von Neumann algebra, arising from the associated codimension-1 foliation of $S^{3}$ with non-trivial Godbillon–V…