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The homology of certain subgroups of the symmetric group with coefficients in \(\text{Lie}(n)\). (English) Zbl 0921.55012

Based on earlier work of the first author with M. Mahowald [Invent. Math. 135, No. 3, 743–788 (1999; Zbl 0997.55016)] calculating the homology \(H_*(\Sigma_n,{\mathcal L}ie(n))\) of the symmetric group with coefficients in a certain Lie algebra over \({\mathbb Z}/p\), the authors calculate the homology of subgroups of the form \(\Sigma_{n_1} \times \cdots \times \Sigma_{n_k}\) with \(n_1+ \cdots+ n_k=n\), with the same coefficients. The approach is via homotopy theory and relies on Goodwillie’s calculus of functors.

MSC:

55R35 Classifying spaces of groups and \(H\)-spaces in algebraic topology
20J06 Cohomology of groups
55R40 Homology of classifying spaces and characteristic classes in algebraic topology
55P15 Classification of homotopy type

Citations:

Zbl 0997.55016
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References:

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