Skyrme fields, multi-instantons and the $SU(\infty )$-Toda equation
We construct Skyrme fields from holonomy of the spin connection of multi-Taub-NUT instantons with the centres positioned along a line in R3. The domain of our Skyrme fields is the space of orbits of the axial symmetry of the multi-Taub-NUT instantons. We obtain an expression for the induced Einstein-Weyl metric on the space and its associated solution to the $SU(\infty )$-Toda equation.