6 problems

Consider reduced spin graphs of rank $2$, together with their systems of invariants and the induced notion of $k$-equivalence. The preceding result shows that, for fixed nonzero in…

Different algebraic plumbing graphs can yield equivalent systems of invariants. To address this, a reduced form is introduced for the plumbing graphs, and the associated system of…

Gukov's conjecture. For any tree and labeling such that $M$ is positive definite, $\widehat{Z}_{{\boldsymbol{a}}}(q)$ is a quantum modular form.

Assume that $(X,0)$ is a normal surface singularity whose link $M$ is a $cQ$-homology sphere. Let $p_g$ be the geometric genus, let $csigma_{can}$ be the canonical $cspin^c$ struct…

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 decorated plumbing graph associated with a fixed geometric object, and let $c(G)$ be the number of independent cycles in $G$, namely the rank of $H_1(|G|)$, where…