Abstract

this paper is to illustrate the use of a well-known technique of algebraic topology, the Hopf trace formula, as a tool in computing homology representations of posets. Inspired by a recent paper of Bjorner and Lov'asz ([BL]), we apply this tool to derive information about the homology representation of the symmetric group Sn on a class of subposets of the partition lattice \Pi n : The majority of these subposets are not Cohen-Macaulay. Techniques for such computations have taken on an added significance because of recent developments in the theory of subspace arrangements, in particular the equivariant Goresky-MacPherson formula of [SWe1]. The latter formula reduces the calculation of the representation on the cohomology of the complement of a subspace arrangement to the problem of computing the homology representation on the intersection lattice of the arrangement

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