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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 m, m 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.

Keywords
operad, long knot
Mathematical Subject Classification 2010
Primary: 18D50, 55P48
Secondary: 18G55, 57Q45
References
Publication
Received: 7 December 2010
Revised: 6 February 2012
Accepted: 9 February 2012
Published: 21 May 2012
Proposed: Paul Goerss
Seconded: Haynes Miller, Ralph Cohen
Authors
William Dwyer
Department of Mathematics
University of Notre Dame
Notre Dame IN 46556
USA
http://www.nd.edu/~wgd
Kathryn Hess
Institut de Géométrie, algèbre et topologie (IGAT)
École Polytechnique Fédérale de Lausanne
CH-1015 Lausanne
Switzerland
http://sma.epfl.ch/~hessbell/