Fix a Calabi–Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. Joyce's generalised DT invariants count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we also express rank r DT invariants in terms of rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by S-duality to be governed by (vector-valued mock) modular forms.

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