Long Knots and Maps between Operads
نویسنده
چکیده
We identify the space of tangentially straightened long knots in R, 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.
منابع مشابه
On the homology of the spaces of long knots
Keywords: discriminant of the space of knots, bialgebra of chord diagrams, Hochschild complex, operads of Poisson – Gerstenhaber – Batalin-Vilkovisky algebras. This paper is a more detailed version of [T1], where the first term of the Vassiliev spectral sequence (computing the homology of the space of long knots in R d , d ≥ 3) was described in terms of the Hochschild homology of the Poisson al...
متن کاملKnots, Operads and Double Loop Spaces
We show that the space of long knots in an euclidean space of dimension larger than three is a double loop space, proving a conjecture by Sinha. We also construct a double loop space structure on framed long knots, and show that the map forgetting the framing is not a double loop map in odd dimension. However there is always such a map in the reverse direction expressing the double loop space o...
متن کاملConstructions of En operads
Throughout this talk I will use the following conventions and notations. I will primarily consider operads in the category of compactly generated Hausdorff topological spaces having the homotopy type of CW-complexes. When I refer to simplicial operads or operads in the category of posets, it will be understood that they can be converted to topological operads by taking geometric realization or ...
متن کاملLocalization of Algebras over Coloured Operads
We give sufficient conditions for homotopical localization functors to preserve algebras over coloured operads in monoidal model categories. Our approach encompasses a number of previous results about preservation of structures under localizations, such as loop spaces or infinite loop spaces, and provides new results of the same kind. For instance, under suitable assumptions, homotopical locali...
متن کاملBar-cobar Duality for Operads in Stable Homotopy Theory
We extend bar-cobar duality, defined for operads of chain complexes by Getzler and Jones, to operads of spectra in the sense of stable homotopy theory. Our main result is the existence of a Quillen equivalence between the category of reduced operads of spectra (with the projective model structure) and a new model for the homotopy theory of cooperads of spectra. The crucial construction is of a ...
متن کامل