Partition Complexes, Tits Buildings and Symmetric Products

2001/01/01 by G. Z. Arone, Gregory Arone, W. G. Dwyer · 5 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · doi:10.1112/s0024611500012715

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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• Augmented Gamma-spaces, the stable rank filtration, and a bu-analogue of the Whitehead Conjecture
• A branching rule for partition complexes
• The Goodwillie calculus of polyhedral products
• P-Toral Approximations Compute Bredon Homology
• A guide to telescopic functors

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