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McCarthy, Randy Mauer-Oats, Andrew John 2015-09-28T15:19:36Z 2015-09-28T15:19:36Z 10000-01-01 2002 2002 "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." Made available in DSpace on 2015-09-28T15:19:36Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3070382.pdf: 5697008 bytes, checksum: 16663b339620ac70845e4576c860ae29 (MD5) Previous issue date: 2002 Embargo set by: Seth Robbins for item 88081 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 114 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002. http://hdl.handle.net/2142/86800 (MiAaPQ)AAI3070382 eng Mathematics Goodwillie Calculi text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.