Abstract
This paper extends hyperkähler Floer theory with flat target manifolds from the case where the source is a 3-sphere or 3-torus, equipped with a standard frame, to the case where the source is a general closed orientable 3-manifold, equipped with a regular divergence-free frame. Regular divergence-free frames are characterized by the nonexistence of nonconstant solutions to the unperturbed linear Fueter equation. They form a dense open subset of the space of all divergence-free frames. A gauged version of the Fueter equation is introduced, which unifies various geometric equations in gauge theory.
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