Operads and knot spaces

Sinha, Dev

doi:10.1090/S0894-0347-05-00510-2

Operads and knot spaces
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by Dev P. Sinha

J. Amer. Math. Soc. 19 (2006), 461-486

DOI: https://doi.org/10.1090/S0894-0347-05-00510-2

Published electronically: November 15, 2005

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Abstract:

We model the homotopy fiber $E_m$ of the inclusion of the space of long knots in dimension $m$ into the corresponding space of immersions, through an operad structure on compactifications of configuration spaces. Development of this operad structure involves defining an operad structure on the simplicial model for the two-sphere. We apply results of McClure and Smith to deduce the existence of a two-cubes action on $E_m$.

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