Volume 16, issue 2 (2012)

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Long knots and maps between operads

William Dwyer and Kathryn Hess

Geometry & Topology 16 (2012) 919–955
Abstract

We identify the space of tangentially straightened long knots in ${ℝ}^{m}$, $m\ge 4$, as the double loops on the space of derived operad maps from the associative operad into a version of the little $m$–disk operad. This verifies a conjecture of Kontsevich, Lambrechts and Turchin.