Long knots and maps between operads

Abstract

We identify the space of tangentially straightened long knots in R^m, for m greater than or equal to 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.

37 pages

References in corpus (1)

• Classification spaces of maps in model categories

Cited by in corpus (23)

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• A Model Structure on the Category of Topological Categories
• Relative left properness of colored operads
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• The homotopy theory of operad subcategories
• Galois symmetries of knot spaces
• Delooping of high-dimensional spaces of string links
• BV-structures on the homology of the framed long knot space
• Embedding calculus and grope cobordism of knots
• Quillen cohomology of enriched operads
• Low stages of the Taylor tower for r-immersions
• A delooping of the space of string links
• A Weiss-Williams theorem for spaces of embeddings and the homotopy type of spaces of long knots
• An Application of the $h$-principle to Manifold Calculus
• Spaces of Operad Structures
• On the moduli space of A-infinity structures
• Goodwillie's cosimplicial model for the space of long knots and its applications
• Stabilization of the category of simplicial objects in CAT