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Partition Complexes, Tits Buildings and Symmetric Products
Author(s) -
Arone G. Z.,
Dwyer W. G.
Publication year - 2001
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012715
Subject(s) - mathematics , functor , partition (number theory) , affine transformation , idempotence , pure mathematics , identity (music) , tower , symmetric group , algebra over a field , combinatorics , physics , acoustics , civil engineering , engineering
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.