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Tyler Lawson
The Plus Construction
Abstract:
The plus construction is a (homotopy invariant) construction we apply to
connected spaces where pi_1 contains a perfect normal subgroup. It has
several descriptions and is related, for example, to Bousfield
localization with respect to integral homology. The Kan loop group
functor G(X), however, gives an equivalence between the homotopy category
of reduced simplicial spaces and the homotopy category of simplicial
groups, so there must be an expression of the plus construction in terms
of simplicial groups. In these circumstances, integral homology is
replaced by Quillen homology.
In this talk I will introduce the plus construction, discuss the version
for simplicial groups, and talk about how this generalizes to other kinds
of objects such as simplicial rings or other "ring objects".
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