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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 $$p \lambda_{i}(E) = \kappa_{i(p-1)-1}(E) \;\in \;H^*(B; {\mathbb Z}/p^{2})$$.

##### MSC:
 55R40 Homology of classifying spaces and characteristic classes in algebraic topology
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##### References:
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