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Title:Goodwillie Calculi
Author(s):Mauer-Oats, Andrew John
Doctoral Committee Chair(s):McCarthy, Randy
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Abstract:We define an "algebraic" version of the Goodwillie tower, Pdn F(X), that depends only on the behaviour of F on coproducts of X. When F is a functor to connected spaces or grouplike H-spaces, the functor Pdn F is the base of a fibration &vbm0;⊥*+1F&vbm0;→ F→P dnF, whose fiber is the simplicial space associated to a cotriple ⊥ built from the (n + 1)st cross effect of the functor F. From this we derive a spectral sequence converging to pi* Pdn F. When the connectivity of X is large enough (for example, when F is the identity functor and X is simply connected), the algebraic Goodwillie tower agrees with the ordinary (topological) Goodwillie tower, so this theory gives a way of studying the Goodwillie approximation to a functor F in many interesting cases. As an application, we show the sense in which Curtis's filtration of a simplicial group by the lower central series is "pi 0" of the filtration provided by Goodwillie calculus.
Issue Date:2002
Description:114 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002.
Other Identifier(s):(MiAaPQ)AAI3070382
Date Available in IDEALS:2015-09-28
Date Deposited:2002

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