no. 2
From maps between coloured operads to Swiss-Cheese algebras
[Construction d’une algèbre Swiss-Cheese à partir d’un morphisme d’opérades colorées]
Ducoulombier, Julien1
1 ETH Zurich Ramistrasse 101 809 Zurich (Switzerland)
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 ℝ d vers ℝ 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 ℝ d to ℝ n is an 𝒮𝒞 d+1 -algebra.

Reçu le :
Révisé le :
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DOI : 10.5802/aif.3175
Classification : 18D50, 55P35, 57Q45
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

1 ETH Zurich Ramistrasse 101 809 Zurich (Switzerland)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3175/

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