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steinberg

Proceedings of the London Mathematical Society (1)

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PARTITION COMPLEXES, TITS BUILDINGS AND SYMMETRIC PRODUCTS
G. Z. ARONE, W. G. DWYER
Journal:

Proceedings of the London Mathematical Society / Volume 82 / Issue 1 / January 2001

Published online by Cambridge University Press:

12 January 2001, pp. 229-256

Print publication:

January 2001
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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.