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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Operads and knot spaces


Author: Dev P. Sinha
Journal: J. Amer. Math. Soc. 19 (2006), 461-486
MSC (2000): Primary 57Q45, 18D50, 57M27
Published electronically: November 15, 2005
MathSciNet review: 2188133
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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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Additional Information

Dev P. Sinha
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403

DOI: http://dx.doi.org/10.1090/S0894-0347-05-00510-2
PII: S 0894-0347(05)00510-2
Keywords: Knot spaces, operads, embedding calculus
Received by editor(s): September 20, 2004
Published electronically: November 15, 2005
Additional Notes: The author is partially supported by NSF grant DMS-0405922.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.