9 problems

Let the 4-dimensional topological surgery conjecture be the assertion that, for a 4-dimensional Poincaré pair $(X,N)$, the sequence … is exact. In the link formulation, let…

Disk embedding up to s-cobordism conjecture. There should be an $s$-cobordism of the immersion $A$ to a topological embedding.

Boundary-universal cork conjecture. There is no $\partial$-universal cork.

Universal cork conjecture. There is no universal cork, i.e. no cork $(U,f_U)$ relating every exotic pair of simply-connected, closed $4$-manifolds.

Disc embedding conjecture. The circles $f_i(S^1)$ bound disjointly embedded discs in $M$ with transverse spheres, inducing the same framing on $f_i(S^1)$ as the $f_i$.

$s$-cobordism conjecture. There is a homeomorphism

Topological surgery conjecture. The map is topologically normally bordant rel. boundary to a homotopy equivalence if and only if the surgery obstruction in…

Topological surgery conjecture. There exist a topological $4$-manifold $N$, with $\partial N=\partial M$, and a homotopy equivalence $\beta$ extending $\alpha$:

Hambleton–Teichner decomposition conjecture. Every smoothable 4-manifold is topologically homeomorphic to a connected sum