5 problems

Gordon's conjecture. The connected-sum Heegaard splitting $\mathcal{V}\cup_S\mathcal{W}$ is stabilized if and only if at least one of the summand splittings

Let $U$ be a homology $4$-sphere admitting a handle structure containing no $3$-handles. Weak generalized Property R equivalence conjecture. The weak generalized Property R conject…

Weak generalized Property R conjecture. Then

Let $\Delta$ be Freedman's contractible topological $4$-manifold whose boundary is the Poincaré homology sphere, and let $H$ be a handlebody with interior homeomorphic to…

Let $L$ be a $g$-component link embedded as a cut system on a genus-$g$ Heegaard surface in $\#^j(S^1 \times S^2)$, and suppose that surface-framed surgery on $L$ yields…