From maps between coloured operads to Swiss-Cheese algebras  [ Construction d’une algèbre Swiss-Cheese à partir d’un morphisme d’opérades colorées ]
Annales de l'Institut Fourier, Tome 68 (2018) no. 2, pp. 661-724.

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 1. Nous sommes alors en mesure d’identifier le couple formé des plongements longs et de l’approximation polynomiale des (l)-immersions de d vers n à une algèbre sous l’opérade Swiss-Cheese de dimension d+1.

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 𝒮𝒞 1 . Thereafter, we show that the pair formed by the space of long embeddings and the manifold calculus limit of (l)-immersions from d to n is an 𝒮𝒞 d+1 -algebra.

Reçu le : 2016-06-06
Révisé le : 2017-04-24
Accepté le : 2017-07-12
Publié le : 2018-04-17
DOI : https://doi.org/10.5802/aif.3175
Classification : 18D50,  55P35,  57Q45
Mots clés : opérades colorées, espaces de lacets, espaces de plongements, catégorie modèle
@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'institut Fourier},
     volume = {68},
     number = {2},
     year = {2018},
     doi = {10.5802/aif.3175},
     language = {en},
     url = {archive.numdam.org/item/AIF_2018__68_2_661_0/}
}
Ducoulombier, Julien. From maps between coloured operads to Swiss-Cheese algebras. Annales de l'Institut Fourier, Tome 68 (2018) no. 2, pp. 661-724. doi : 10.5802/aif.3175. http://archive.numdam.org/item/AIF_2018__68_2_661_0/

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