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Title:  Goodwillie Calculi 
Author(s):  MauerOats, Andrew John 
Doctoral Committee Chair(s):  McCarthy, Randy 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
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 Hspaces, 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 
Type:  Text 
Language:  English 
Description:  114 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2002. 
URI:  http://hdl.handle.net/2142/86800 
Other Identifier(s):  (MiAaPQ)AAI3070382 
Date Available in IDEALS:  20150928 
Date Deposited:  2002 
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Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois