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The permutoassociahedron, Mac Lane’s coherence theorem and asymptotic zones for the KZ equation. (English) Zbl 0812.18003
All possible bracketings of $n$ symbols in all possible orders are exhibited as vertices of a combinatorial CW-complex $K{P}_{n}$. It is clearly relevant to the coherence of symmetric monoidal categories, yet also fits nicely into Drinfel’d’s study of the Knizhnik-Zamolodchikov equations and into the analysis of the Grothendieck-Knudsen moduli space of stable $n$-pointed curves of genus 0.

##### MSC:
 18D10 Monoidal, symmetric monoidal and braided categories 14D10 Arithmetic ground fields (finite, local, global) 35Q99 PDE of mathematical physics and other areas 19D23 Symmetric monoidal categories ($K$-theory)