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Secondary characteristic classes of surface bundles. (English) Zbl 1166.55004
A surface bundle is a smooth fibre bundle \(\pi :E \rightarrow B\) with closed oriented two-dimensional fibres. The Miller-Morita-Mumford characteristic classes associate to such a bundle classes \(\kappa_{i} \;\in \;H^{2i}(B; {\mathbb Z})\). The author shows that \(k_{i}\) is divisible by \(p^{2}\) if and only if \(i+1\) is divisible by \(p(p-1)\). The proof introduces new characteristic classes \(\lambda_{i}\) with the property that \(p \lambda_{i}(E) = \kappa_{i(p-1)-1}(E) \;\in \;H^*(B; {\mathbb Z}/p^{2})\).

55R40 Homology of classifying spaces and characteristic classes in algebraic topology
Full Text: DOI arXiv
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