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PARTITION COMPLEXES, TITS BUILDINGS AND SYMMETRIC PRODUCTS

Published online by Cambridge University Press:  12 January 2001

G. Z. ARONE  and
W. G. DWYER
G. Z. ARONE
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA, arone@math.uchicago.edu
W. G. DWYER
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA, dwyer.1@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 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.

Keywords

buildingspartitionssymmetricSteinbergGoodwillie
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 82 , Issue 1 , January 2001 , pp. 229 - 256
Copyright
2001 London Mathematical Society

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