3 problems

Let $Y$ be a negative-definite plumbed manifold, let $\spc{Y}$ denote its set of $spin^c$ structures, and let $\Delta_b$ be the corresponding invariant for $b\in \spc{Y}$. Let…

Let $\Gamma=(V,E,(w_v)_{v\in V})$ be a finite tree with integral vertex weights, and let $W$ be its negative-definite linking matrix. Let $M(\Gamma)$ be the integral homology spher…

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…