Considering the MO question Connes-Kreimer Hopf algebra and cosmic Galois group, can you calculate the cosmic Galois group of a "bundle" over a quintic threefold and relate it with the quintics' Gromov-Witten invariants as explained by Cox and Katz in Mirror symmetry and algebraic geometry? If so, then how is this done?
Edit: Also, the Seiberg-Witten invariants of these quintic threefolds might have been formally derived from the Gromov-Witten invariants according to Taubes by now? Is that true?
