Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Saturated fusion systems as idempotents in the double Burnside ring   We give a new, unexpected characterization of saturated fusion systems on a
p-group S in terms of idempotents in the p-local double Burnside ring of S that
satisfy a Frobenius reciprocity relation, and reformulate fusion-theoretic
phenomena in the language of idempotents. Interpreting our results in stable
homotopy, we answer a long-standing question on stable splittings of
classifying spaces of finite groups, and generalize the Adams--Wilkerson
criterion for recognizing rings of invariants in the cohomology of an
elementary abelian p-group. This work is partly motivated by a conjecture of
Haynes Miller which proposes retractive transfer triples as a purely
homotopy-theoretic model for p-local finite groups. We take an important step
toward proving this conjecture by showing that a retractive transfer triple
gives rise to a p-local finite group when two technical assumptions are made,
thus reducing the conjecture to proving those two assumptions.

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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cs