COLLAPSIBILITY OF ( n)=Sn AND SOME RELATED CW COMPLEXES
نویسنده
چکیده
Let ∆(Πn) denote the order complex of the partition lattice. The natural Sn-action on the set [n] induces an Sn-action on ∆(Πn). We show that the regular CW complex ∆(Πn)/Sn is collapsible. Even more, we show that ∆(Πn)/Sn is collapsible, where Π∆ 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 Sn-representation on H∗(∆(Πn)).
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