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arxiv: math/0407039 · v3 · submitted 2004-07-03 · 🧮 math.AT · math.QA

Operads and knot spaces

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keywords operadknotkontsevichmodelspacesactionapplicationscategory
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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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