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Article Dans Une Revue Journal de l'École polytechnique — Mathématiques Année : 2021

The diagonal of the associahedra

Résumé

This paper introduces a new method to solve the problem of the approximation of the diagonal for face-coherent families of polytopes. We recover the classical cases of the simplices and the cubes and we solve it for the associahedra, also known as Stasheff polytopes. We show that it satisfies an easy-to-state cellular formula. For the first time, we endow a family of realizations of the associahedra (the Loday realizations) with a topological and cellular operad structure; it is shown to be compatible with the diagonal maps.

Dates et versions

hal-02378812 , version 1 (25-11-2019)

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Naruki Masuda, Hugh Thomas, Andy Tonks, Bruno Vallette. The diagonal of the associahedra. Journal de l'École polytechnique — Mathématiques, 2021, 8, pp.121-146. ⟨10.5802/jep.142⟩. ⟨hal-02378812⟩
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