Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Kervaire-Milnor invariant in the stable classification of spin
  4-manifolds   We consider the role of the Kervaire-Milnor invariant in the classification
of closed, connected, spin 4-manifolds up to stabilisation by connected sums
with copies of $S^2 \times S^2$. This stable classification is detected by a
spin bordism group over the classifying space $B\pi$ of the fundamental group.
Part of the computation of this bordism group via an Atiyah-Hirzebruch spectral
sequence is determined by a collection of codimension two Arf invariants. We
show that these Arf invariants can be computed by the Kervaire-Milnor invariant
evaluated on certain elements of $\pi_2$. In particular this yields a new
stable classification of spin 4-manifolds with 2-dimensional fundamental
groups.

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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph