Mukai duality applied fibre-by-fibre produces a canonical dual Donaldson adiabatic fibration for K3-fibred G2 manifolds, and a Nahm transform maps twisted G2 instantons between the two sides.
A hyper-K¨ ahler Fourier transform
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Mukai duality on adiabatic coassociative fibrations
Mukai duality applied fibre-by-fibre produces a canonical dual Donaldson adiabatic fibration for K3-fibred G2 manifolds, and a Nahm transform maps twisted G2 instantons between the two sides.