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PARTITION COMPLEXES, TITS BUILDINGS AND SYMMETRIC PRODUCTS

  • G. Z. ARONE (a1) and W. G. DWYER (a2)

Abstract

We construct a homological approximation to the partition complex, and identify it as the Tits building. This gives a homological relationship between the symmetric group and the affine group, leads to a geometric tie between symmetric powers of spheres and the Steinberg idempotent, and allows us to use the self-duality of the Steinberg module to study layers in the Goodwillie tower of the identity functor. 2000 Mathematics Subject Classification: 55N25, 55S15, 20B30, 55P25.

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Keywords

PARTITION COMPLEXES, TITS BUILDINGS AND SYMMETRIC PRODUCTS

  • G. Z. ARONE (a1) and W. G. DWYER (a2)

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