From maps between coloured operads to Swiss-Cheese algebras

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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.