{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/98276"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/98276","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Computing the Goodwillie-Taylor tower for discrete modules","abstract":"A functor from finite sets to chain complexes is called atomic if it is completely determined by its value on a particular set. We present a new resolution for these atomic functors, which allows us to easily compute their Goodwillie polynomial approximations. By a rank filtration, any functor from finite sets to chain complexes is built from atomic functors. Computing the linear approximation of an atomic functor is a classic result involving partition complexes. Robinson constructed a bicomplex, which can be used to compute the linear approximation of any functor. We hope to use our new resolution to similarly construct bicomplexes that allow us to compute polynomial approximations for any functor from finite sets to chain complexes.","abstract_html":"A functor from finite sets to chain complexes is called atomic if it is completely determined by its value on a particular set. We present a new resolution for these atomic functors, which allows us to easily compute their Goodwillie polynomial approximations. By a rank filtration, any functor from finite sets to chain complexes is built from atomic functors. Computing the linear approximation of an atomic functor is a classic result involving partition complexes. Robinson constructed a bicomplex, which can be used to compute the linear approximation of any functor. We hope to use our new resolution to similarly construct bicomplexes that allow us to compute polynomial approximations for any functor from finite sets to chain complexes.","abstract_has_math":false,"creators":["Tebbe, Amelia Nora"],"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","Ando, Matt","Rezk, Charles","Malkiewich, Cary"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-09-29T16:39:45Z","date_published":"2017-09-29T16:39:45Z","updated_at":"2026-07-22T22:24:35Z","subjects":["Functor calculus","Goodwillie calculus","Discrete modules","Atomic functors","Finite sets","Rank filtration","Algebraic topology","Homotopy theory"],"languages":["en"],"rights":["Copyright 2017 Amelia Tebbe"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/98276","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["McCarthy, Randy","Ando, Matt","Rezk, Charles","Malkiewich, Cary"]},{"key":"dc:creator","label":"Author","values":["Tebbe, Amelia Nora"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-09-29T16:39:45Z","2019-09-30T09:15:20Z","2017-07-11","2017-08"]},{"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":["Functor calculus","Goodwillie calculus","Discrete modules","Atomic functors","Finite sets","Rank filtration","Algebraic topology","Homotopy theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Amelia Tebbe"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/98276"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A functor from finite sets to chain complexes is called atomic if it is completely determined by its value on a particular set. We present a new resolution for these atomic functors, which allows us to easily compute their Goodwillie polynomial approximations. By a rank filtration, any functor from finite sets to chain complexes is built from atomic functors. Computing the linear approximation of an atomic functor is a classic result involving partition complexes. Robinson constructed a bicomplex, which can be used to compute the linear approximation of any functor. We hope to use our new resolution to similarly construct bicomplexes that allow us to compute polynomial approximations for any functor from finite sets to chain complexes.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-08-01","The student, Amelia Tebbe, accepted the attached license on 2017-07-11 at 14:57.","The student, Amelia Tebbe, submitted this Dissertation for approval on 2017-07-11 at 15:10.","This Dissertation was approved for publication on 2017-07-11 at 15:51.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11402 on 2017-09-29 at 11:18:54","Made available in DSpace on 2017-09-29T16:39:45Z (GMT). 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We present a new resolution for these atomic functors, which allows us to easily compute their Goodwillie polynomial approximations. By a rank filtration, any functor from finite sets to chain complexes is built from atomic functors. Computing the linear approximation of an atomic functor is a classic result involving partition complexes. Robinson constructed a bicomplex, which can be used to compute the linear approximation of any functor. We hope to use our new resolution to similarly construct bicomplexes that allow us to compute polynomial approximations for any functor from finite sets to chain complexes.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-08-01","The student, Amelia Tebbe, accepted the attached license on 2017-07-11 at 14:57.","The student, Amelia Tebbe, submitted this Dissertation for approval on 2017-07-11 at 15:10.","This Dissertation was approved for publication on 2017-07-11 at 15:51.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11402 on 2017-09-29 at 11:18:54","Made available in DSpace on 2017-09-29T16:39:45Z (GMT). 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