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- W278350446 abstract "In [arXiv:1609.02636], we introduced picture groups and computed the cohomology of the picture group of type $A_n$. This is the same group what was introduced by Loday [21] where he called it the Stasheff group. In this paper, we give an elementary combinatorial interpretation of the category associated to $A_n$ by the general construction given in [arXiv.1706.02041] and prove that the classifying space of this category is locally $CAT(0)$ and thus a $K(pi,1)$. We prove a more general statement that classifying spaces of certain cubical categories are locally $CAT(0)$. The objects of our category are the classical noncrossing partitions introduced by Kreweras [20]. The morphisms are binary forests. This paper is independent of [14] and [18] except in the last section where we use [14] to compare our category with the category with the same name given by Hubery and Krause [9]." @default.
- W278350446 created "2016-06-24" @default.
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- W278350446 date "2014-11-01" @default.
- W278350446 modified "2023-09-26" @default.
- W278350446 title "The category of noncrossing partitions" @default.
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- W278350446 doi "https://doi.org/10.48550/arxiv.1411.0196" @default.
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