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2004 Diagonals on the permutahedra, multiplihedra and associahedra
Samson Saneblidze, Ronald Umble
Homology Homotopy Appl. 6(1): 363-411 (2004).

Abstract

We construct an explicit diagonal $\Delta_{P}$ on the permutahedra $P.$ Related diagonals on the multiplihedra $J$ and the associahedra $K$ are induced by Tonks' projection $P\rightarrow K$ [19] and its factorization through $J.$ We introduce the notion of a permutahedral set $% \mathcal{Z}$ and lift $\Delta_{P}$ to a diagonal on $\mathcal{Z}$. We show that the double cobar construction $\Omega^{2}C_{\ast}(X)$ is a permutahedral set; consequently $\Delta_{P}$ lifts to a diagonal on $% \Omega^{2}C_{\ast}(X)$. Finally, we apply the diagonal on $K$ to define the tensor product of $A_{\infty}$-(co)algebras in maximal generality.

Citation

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Samson Saneblidze. Ronald Umble. "Diagonals on the permutahedra, multiplihedra and associahedra." Homology Homotopy Appl. 6 (1) 363 - 411, 2004.

Information

Published: 2004
First available in Project Euclid: 13 February 2006

zbMATH: 1069.55015
MathSciNet: MR2118493

Subjects:
Primary: 55U05
Secondary: 05A18 , 52B05 , 55P35 , 81T30

Rights: Copyright © 2004 International Press of Boston

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Vol.6 • No. 1 • 2004
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