Derived spectrum invariance for 3-manifolds

A derived spectrum is the spectrum associated with the derived critical-locus construction of a potential for the moduli space of $\mathop{SL}(2,\mathbb{C})$ representations of a 3-manifold $Y$, obtained after choosing a Heegaard splitting. Derived spectrum invariance conjecture. The derived spectrum of $f$ is an invariant of $Y$, independent of the way in which $Y$ is constructed. The conjecture proposes that the derived spectrum does not depend on the auxiliary Heegaard splitting or the resulting presentation of the derived critical locus; the paper suggests that an alternative Landau–Ginzburg construction might provide a proof.