Long knots and maps between operads

Dwyer, William¹ ; Hess, Kathryn²

¹ Department of Mathematics, University of Notre Dame, Notre Dame IN 46556, USA
² Institut de Géométrie, algèbre et topologie (IGAT), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

Geometry & topology, Tome 16 (2012) no. 2, pp. 919-955.

Résumé

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.

Détail

DOI : 10.2140/gt.2012.16.919

Classification : 18D50, 55P48, 18G55, 57Q45
Keywords: operad, long knot

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