Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Secondary Characteristic Classes of Surface Bundles   The Miller-Morita-Mumford classes associate to an oriented surface bundle
$E\to B$ a class $\kappa_i(E) \in H^{2i}(B;\Z)$. In this note we define for
each prime $p$ and each integer $i\geq 1$ a secondary characteristic class
$\lambda_i(E) \in H^{2i(p-1)-2}(B;\Z)/\Z\kappa_{i(p-1)-1}$. The mod $p$
reduction $\lambda_i(E) \in H^*(B; \F_p)$ has zero indeterminacy and satisfies
$p\lambda_i(E) = \kappa_{i(p-1)-1}(E) \in H^*(B;\Z/p^2)$.

9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg