On the geometric nature of characteristic classes of surface bundles

Each Morita–Mumford–Miller (MMM) class en assigns to each genus g ≥ 2 surface bundle Σg → E 2n+2 → M an integer en (E → M) := 〈en, [M ]〉 ∈ Z. We prove that when n is odd the number en (E → M) depends only on the diffeomorphism type of E, not on g, M or the map E → M . Applying deep results of Pontryagin and Novikov, we generalize this to prove that en (E… CONTINUE READING