Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H-Space and Loop Space Structures for Intermediate Curvatures   For dimensions $n\geq 3$ and $k\in\{2, \cdots, n\}$, we show that the space
of metrics of $k$-positive Ricci curvature on the sphere $S^{n}$ has the
structure of an $H$-space with a homotopy commutative, homotopy associative
product operation. We further show, using the theory of operads and results of
Boardman, Vogt and May that the path component of this space containing the
round metric is weakly homotopy equivalent to an $n$-fold loop space.

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
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The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc