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 Title: Goodwillie Calculi Author(s): Mauer-Oats, Andrew John Doctoral Committee Chair(s): McCarthy, Randy Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign 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 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 Type: Text Language: English Description: 114 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002. URI: http://hdl.handle.net/2142/86800 Other Identifier(s): (MiAaPQ)AAI3070382 Date Available in IDEALS: 2015-09-28 Date Deposited: 2002
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