9 problems

Let $\Sigma$ be obtained by splicing homology spheres $\Sigma_1$ and $\Sigma_2$ along an edge of a splice diagram satisfying the semigroup condition. Let $F$, $F_1$, and $F_2$ be t…

Complete-intersection semigroup-condition conjecture. If $X$ is a complete intersection, then $\Delta$ satisfies the semigroup condition.

Let $(X,o)$ be a Gorenstein surface singularity with integral homology sphere link, and let its splice diagram encode the topology of the link. Gorenstein splice-type conjecture.…

Let $(X,o)$ be a ${\mathbb Q}$-Gorenstein normal surface singularity with ${\mathbb Q}$-homology sphere link, and let $\Delta$ be the splice diagram associated to its resolution gr…

Let $(X,o)$ be a ${\mathbb Q}$-Gorenstein surface singularity with ${\mathbb Q}$-homology sphere link, and let its resolution graph be equipped with the associated discriminant-gro…

Let $\Delta$ be the splice diagram associated to a ${\mathbb Q}$-Gorenstein surface singularity with ${\mathbb Q}$-homology sphere link. For a node $v$ and an adjacent edge $e$, le…

Milnor fiber conjecture. The Milnor fiber of $(X,o)$ is obtained by a four-dimensional splicing operation from the Milnor fibers associated to $\Gamma_a$ and $\Gamma_b$.

Universal abelian cover conjecture. The link of this complete intersection singularity is the universal abelian cover of $\Sigma$.

Splice-diagram decomposition conjecture. The Milnor fiber $F$ is homeomorphic to the result $\overline F$ of pasting