Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coproducts in brane topology   We extend the loop product and the loop coproduct to the mapping space from
the $k$-dimensional sphere, or more generally from any $k$-manifold, to a
$k$-connected space with finite dimensional rational homotopy group, $k\geq 1$.
The key to extending the loop coproduct is the fact that the embedding
$M\rightarrow M^{S^{k-1}}$ is of "finite codimension" in a sense of Gorenstein
spaces. Moreover, we prove the associativity, commutativity, and Frobenius
compatibility of them.

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
9
The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con