Abstract
We construct a combinatorial CW-complex KP n whose vertices correspond to all possible bracketings of all possible permutations of n letters A 1,…, A n. This structure is implicitly present in Mac Lane's coherence theorem for symmetric and braided monoidal categories. It also fits very naturally in the framework of the study of Knizhnik-Zamolodchikov (KZ) equations initiated by V. Drinfel'd. We show that KP n is a combinatorial ( n − 1)-ball and establish its connection with the Grothendieck-Knudsen moduli space of stable n-pointed curves of genus 0.
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