Partition Complexes, Tits Buildings and Symmetric Products |
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| Authors: | Arone G Z; Dwyer W G |
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| Institution: | Department of Mathematics, University of Chicago Chicago, IL 60637, USA; e-mail: arone{at}math.uchicago.edu
Department of Mathematics, University of Notre Dame Notre Dame, IN 46556, USA; e-mail: dwyer.1{at}nd.edu |
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| Abstract: | We construct a homological approximation to the partition complex,and identify it as the Tits building. This gives a homologicalrelationship between the symmetric group and the affine group,leads to a geometric tie between symmetric powers of spheresand the Steinberg idempotent, and allows us to use the self-dualityof the Steinberg module to study layers in the Goodwillie towerof the identity functor. 2000 Mathematics Subject Classification:55N25, 55S15, 20B30, 55P25. |
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| Keywords: | buildings partitions symmetric Steinberg Goodwillie |
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