Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operads and knot spaces   We show that the Kontsevich operad, as an operad with multiplication,
provides a model for the Taylor tower of the functor defined by taking the
homotopy fiber of the inclusion of embeddings of an interval in a cube to the
corresponding space of immersions. In developing the Kontsevich operad, we find
an operad structure on the simplicial model for the two-sphere, in the opposite
category to finite sets. Applications of our result include using machinery of
McClure-Smith to produce a little two-disk action on our knot spaces.

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The categories of this paper are: hep-th
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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: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex