Operads and knot spaces

Details Operads and knot spaces Operads and knot spaces

2004-07-03

arxiv.org/abs/math/0407039v3

J. Amer. Math. Soc., 19 (2006) No 2, 461-486

Mathematics

Algebraic Topology

v3. Final (published) version, incorporating referee comments. Binomial operad has been renamed choose-two operad

Scientific paper

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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