Fix a Calabi-Yau 3-fold X satisfying the Bogomolov-Gieseker conjecture of
Bayer-Macr`ı-Toda, such as the quintic 3-fold.
We express Joyce’s generalised DT invariants counting Gieseker semistable sheaves of
any rank r on X in terms of those counting sheaves of rank 1. By the MNOP conjecture
they are therefore determined by the Gromov-Witten invariants of X.