Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic criteria for stable diffeomorphism of spin 4-manifolds   We study closed, connected, spin 4-manifolds up to stabilisation by connected
sums with copies of $S^2 \times S^2$. For a fixed fundamental group, there are
primary, secondary and tertiary obstructions, which together with the signature
lead to a complete stable classification. The primary obstruction exactly
detects $\mathbb{CP}^2$-stable diffeomorphism and was previously related to
algebraic invariants by Kreck and the authors.
  In this article we formulate conjectural relationships of the secondary and
tertiary obstructions with algebraic invariants: the secondary obstruction
should be determined by the (stable) equivariant intersection form and the
tertiary obstruction via a $\tau$-invariant recording intersection data between
2-spheres, with trivial algebraic self-intersection, and their Whitney discs.
  We prove our conjectures for the following classes of fundamental groups:
groups of cohomological dimension at most 3, right-angled Artin groups, abelian
groups, and finite groups with quaternion or abelian 2-Sylow subgroups. We
apply our theory to give a complete algebraic stable classification of spin
$4$-manifolds with fundamental group $\mathbb{Z} \times \mathbb{Z}/2$.

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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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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: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int