Long knots and maps between operads

Dwyer, William; Hess, Kathryn

doi:10.2140/gt.2012.16.919

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Long knots and maps between operads

William Dwyer and Kathryn Hess

Geometry & Topology 16 (2012) 919–955

DOI: 10.2140/gt.2012.16.919

Abstract

We identify the space of tangentially straightened long knots in $ℝ^{m}$ , $m \geq 4$ , 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/

Volume 16, issue 2 (2012)