Partition complexes, Tits buildings and symmetric products
by
G. Z. Arone and W. G. Dwyer
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.