5 problems

Let $X$ be a $\mathbb Z[\mathbb Z]$-homology $S^1\times S^3$, and let $\lambda_{FO}(X)$ be its Furuta–Ohta invariant and $\rho_{FO}(X)$ its Rohlin invariant. Furuta–Ohta congruence…

Let $\Sigma$ and $\Sigma'$ be homology spheres. A simply connected homology cobordism between them is a homology cobordism whose fundamental group is trivial. Simply connected homo…

Let $X$ be a homology $S^1\times S^3$, and let $\rho(X)$ denote its Rohlin invariant and $\lambda_{FO}(X)$ its Furuta–Ohta invariant. Rohlin–Furuta–Ohta conjecture. The Rohlin inva…

Let $X$ be a smooth closed oriented $4$-manifold with $H_*(X;\mathbb Z)=H_*(S^1\times S^3;\mathbb Z)$ and $H_*(\widetilde X;\mathbb Z)=H_*(S^3;\mathbb Z)$, where $\widetilde X$ is…

Let $X$ be a smooth oriented 4-manifold satisfying … Let $\lambda_{\rm FO}(X)$ be the Furuta–Ohta invariant in the normalization used in the paper, and let…