{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86800"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86800","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Goodwillie Calculi","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.\"","abstract_html":""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."","abstract_has_math":false,"creators":["Mauer-Oats, Andrew John"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["McCarthy, Randy"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:36Z","date_published":"2015-09-28T15:19:36Z","updated_at":"2026-07-22T22:26:27Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3070382"],"render_values":[{"text":"(MiAaPQ)AAI3070382","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86800","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["McCarthy, Randy"]},{"key":"dc:creator","label":"Author","values":["Mauer-Oats, Andrew John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:36Z","10000-01-01","2002"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86800","(MiAaPQ)AAI3070382"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"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."]},{"key":"dc:title","label":"Title","values":["Goodwillie Calculi"]}]}],"canonical_facts":{"dc:contributor":["McCarthy, Randy"],"dc:creator":["Mauer-Oats, Andrew John"],"dc:date":["2015-09-28T15:19:36Z","10000-01-01","2002"],"dc:description":["\"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). 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