In the present work, we extract pairs of topological spaces from maps between coloured operads. We prove that those pairs are weakly equivalent to explicit algebras over the one dimensional Swiss-Cheese operad . Thereafter, we show that the pair formed by the space of long embeddings and the manifold calculus limit of -immersions from to is an -algebra.
A partir d’un morphisme d’opérades colorées, on introduit un couple d’espaces topologiques que l’on identifie explicitement à une algèbre sous l’opérade Swiss-Cheese de dimension . Nous sommes alors en mesure d’identifier le couple formé des plongements longs et de l’approximation polynomiale des -immersions de vers à une algèbre sous l’opérade Swiss-Cheese de dimension .
Revised:
Accepted:
Published online:
Keywords: coloured operads, loop spaces, space of knots, model category
Mot clés : opérades colorées, espaces de lacets, espaces de plongements, catégorie modèle
Ducoulombier, Julien 1
@article{AIF_2018__68_2_661_0, author = {Ducoulombier, Julien}, title = {From maps between coloured operads to {Swiss-Cheese} algebras}, journal = {Annales de l'Institut Fourier}, pages = {661--724}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {2}, year = {2018}, doi = {10.5802/aif.3175}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3175/} }
TY - JOUR AU - Ducoulombier, Julien TI - From maps between coloured operads to Swiss-Cheese algebras JO - Annales de l'Institut Fourier PY - 2018 SP - 661 EP - 724 VL - 68 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3175/ DO - 10.5802/aif.3175 LA - en ID - AIF_2018__68_2_661_0 ER -
%0 Journal Article %A Ducoulombier, Julien %T From maps between coloured operads to Swiss-Cheese algebras %J Annales de l'Institut Fourier %D 2018 %P 661-724 %V 68 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3175/ %R 10.5802/aif.3175 %G en %F AIF_2018__68_2_661_0
Ducoulombier, Julien. From maps between coloured operads to Swiss-Cheese algebras. Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 661-724. doi : 10.5802/aif.3175. https://aif.centre-mersenne.org/articles/10.5802/aif.3175/
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