The diagonal of the associahedra

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 eas...

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Bibliographic Details
Published inJournal de l'École polytechnique. Mathématiques Vol. 8; pp. 121 - 146
Main Authors Masuda, Naruki, Thomas, Hugh, Tonks, Andy, Vallette, Bruno
Format Journal Article
LanguageEnglish
Published École polytechnique 01.01.2021
Subjects
Algebraic Topology
Combinatorics
Mathematics
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ISSN2429-7100
2270-518X
DOI10.5802/jep.142

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Summary: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.
ISSN:2429-7100
2270-518X
DOI:10.5802/jep.142