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https://hdl.handle.net/2142/86800
Description
Title
Goodwillie Calculi
Author(s)
Mauer-Oats, Andrew John
Issue Date
2002
Doctoral Committee Chair(s)
McCarthy, Randy
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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."
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