Diagonals on the Permutahedra, Multiplihedra and Associahedra

Samson Saneblidze; Ronald Umble

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Diagonals on the Permutahedra, Multiplihedra and Associahedra

Samson Saneblidze·Ronald Umble

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Abstract

We construct an explicit diagonal Δ_P on the permutahedra P. Related diagonals on the multiplihedra J and the associahedra K are induced by Tonks' projection P --> K and its factorization through J. We introduce the notion of a permutahedral set Z and lift Δ_P to a diagonal on Z. We show that the double cobar construction Ω^2(C_*(X)) is a permutahedral set; consequently Δ_P lifts to a diagonal on Ω^2(C_*(X)). Finally, we apply the diagonal on K to define the tensor product of A_\infty-(co)algebras in maximal generality.

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BibTeX RIS

Samson Saneblidze, Ronald Umble. 2004-08-21. Diagonals on the Permutahedra, Multiplihedra and Associahedra. https://arxiv.org/abs/math/0209109

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