Collapsibility of <IMG ALIGN=MIDDLE HEIGHT=32 WIDTH=89> and some related CW complexes期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Collapsibility of and some related CW complexes

Authors:	Dmitry N Kozlov

Institution:	Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540

Abstract:	Let $\Delta(\Pi _n)$ denote the order complex of the partition lattice. The natural $\mathcal{S}_n$ -action on the set induces an $\mathcal{S}_n$ -action on $\Delta(\Pi _n)$ . We show that the regular CW complex $\Delta (\Pi _n)/\mathcal{S}_n$ is collapsible. Even more, we show that $\Delta (\Pi _n)/\mathcal{S}_n$ is collapsible, where $\Pi _\Delta$ is a suitable type selection of the partition lattice. This allows us to generalize and reprove in a conceptual way several previous results regarding the multiplicity of the trivial character in the $\mathcal{S}_n$ -representation on $H_*(\Delta(\Pi _n))$ .

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