9 problems

Plumbing-graph equivalence conjecture. If $\Gamma_{v_0}$ and $\Gamma'_{v'_0}$ represent the same triplet $(Y,\xi,L)$, then they are related by the blow-ups depicted in Figure.

Let $\{(C_t,o)\}_{t\in(\mathbb{C},0)}$ be a flat deformation of reduced curve singularities. For every $n\in\mathbb{Z}$, let $S_{n,t}$ denote the corresponding space, and let … be…

Functoriality Conjecture. The maps $\{F_{0,n}\}_n$ can be extended to the $S_n$-spaces up to homotopy, in such a way that they induce a degree-zero graded $\mathbb{Z}[U]$-module mo…

Let $\mathcal{O}_2=k[x_1,x_2]$ and let $\mathcal{I}\triangleleft\mathcal{O}_2$ be a finite-codimensional, integrally closed ideal. Let $\mathcal{O}$ denote the ambient module in th…

Let $k[x_1,x_2]$ be the polynomial ring in two variables, and let $\mathcal{I}\triangleleft k[x_1,x_2]$ be a finite-codimensional, integrally closed ideal. Write…

Let $G$ be a plumbing tree, let $Y(G)$ be its associated plumbed 3-manifold, and let $\boldsymbol{\mathbf{\mathit{HF}}}^-(Y(G))$ denote the completed Heegaard Floer homology. Write…

Let $C$ be the algebraic curve whose link is under consideration, and let $\mathcal{L}^{-}$ be its lattice complex. Write $\operatorname{gr}\mathcal{L}^{-}$ for the associated grad…

Let $Y$ be the underlying $3$-manifold of a negative definite plumbing of spheres along a tree, and let its lattice homology be the invariant associated with the plumbing graph. La…

Let $G$ be a plumbing tree, and let $Y_G$ be the corresponding plumbed $3$-manifold. Denote the lattice homology of $G$ by $\mathbb{HF}^{-}(G)$ and the Heegaard Floer homology of…