Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Secondary Stiefel-Whitney class and diffeomorphisms of rational and
  ruled symplectic 4-manifolds   We introduce the secondary Stiefel-Whitney class $\tilde w_2$ of
homotopically trivial diffeomorphisms and show that a homotopically trivial
symplectomorphism of a ruled 4-manifold is isotopic to identity if and only if
the class $\tilde w_2$ vanishes.
  Using this, we give a detailed description of the combinatorial structure of
the diffeotopy group of ruled symplectic 4-manifolds $X$, either minimal or
blown-up, and its action on the homology and homotopy groups $H_2(X,\zz)$,
$\pi_1(X)$, and $\pi_2(X)$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex