> But in fact, I claim, the smooth conception and the analytic conception are equivalent—they arise from the same underlying structure. Conjugation isn’t compl

> But in fact, I claim, the smooth conception and the analytic conception are equivalent—they arise from the same underlying structure. Conjugation isn’t complex-analytic, so the symmetry of i -> -i is broken at that level. Complex manifolds have to explicitly carry around their almost-complex structure largely for this reason.