The ADE Link Conjecture for cyclic branched covers

Let $L$ be a prime, fibred, strongly quasipositive link, and let $cSigma_{\psi}(L)$ denote a cyclic branched cover of $L$. Write $NLS$ for the property of not being an $L$-space, $LO$ for having left-orderable fundamental group, and $CTF$ for supporting a co-orientable taut foliation. An $ADE$ link is the boundary of a plumbing of positive Hopf bands according to one of the Dynkin diagrams $A_m$, $D_m$, $E_6$, $E_7$, or $E_8$.

The $ADE$ Link Conjecture. If $L$ is not an $ADE$ link, then all cyclic branched covers $cSigma_{\psi}(L)$ of $L$ are $NLS$, $LO$, and $CTF$.

The conjecture extends the established $ADE$-link results beyond Seifert links; the source presents it as an aim whose toroidal and hyperbolic cases remain to be proved.