A topological algorithm for the Fourier transform of Stokes data at infinity

We reinterpret a result of T. Mochizuki about the Fourier transform of Stokes data of irregular connections on the Riemann sphere in the language of Stokes local systems due to P. Boalch. We thus obtain a clean topological description of the Stokes matrices of the Fourier transform from infinity to infinity in a large number of cases of one level. In particular, this induces explicit isomorphisms between wild character varieties, in a much larger range of examples than those for which such isomorphisms have previously been written down. We conjecture that these isomorphisms are compatible with the quasi-Hamiltonian structure of the wild character varieties.