{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/42374"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/42374","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 of discrete modules","abstract":"Let $P_m$ and $D_m$ be the $m^{th}$ level and layer of the Goodwillie-Taylor tower for discrete modules. In \\cite{intermont_johnson_mccarthy08} the rank filtration of $D_1F$ is described and the associated spectral sequence is shown to be equivalent to the filtration by rows of the reduced Robinson bicomplex of $F$. We consider the rank filtrations of $P_mF$ and $D_mF$ and give explicit descriptions of the entries of the $E^1$ page of the associated spectral sequences. In the case $m=1$ these entries agree with those of the spectral sequence associated with the reduced Robinson bicomplex.","abstract_html":"Let <span class=\"etd-inline-math\">P<sub>m</sub></span> and <span class=\"etd-inline-math\">D<sub>m</sub></span> be the <span class=\"etd-inline-math\">m<sup>th</sup></span> level and layer of the Goodwillie-Taylor tower for discrete modules. In \\cite{intermont_johnson_mccarthy08} the rank filtration of <span class=\"etd-inline-math\">D<sub>1</sub>F</span> is described and the associated spectral sequence is shown to be equivalent to the filtration by rows of the reduced Robinson bicomplex of $F$. We consider the rank filtrations of <span class=\"etd-inline-math\">P<sub>m</sub>F</span> and <span class=\"etd-inline-math\">D<sub>m</sub>F</span> and give explicit descriptions of the entries of the <span class=\"etd-inline-math\">E<sup>1</sup></span> page of the associated spectral sequences. In the case $m=1$ these entries agree with those of the spectral sequence associated with the reduced Robinson bicomplex.","abstract_has_math":true,"creators":["Lior, Dan"],"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, Matthew","Rezk, Charles","Nevins, Thomas A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-02-03T19:36:43Z","date_published":"2013-02-03T19:36:43Z","updated_at":"2026-07-22T22:25:33Z","subjects":["Goodwillie","Functor Calculus","Taylor Tower","Robinson Bicomplex","Discrete Module","Discrete Functor"],"languages":["en"],"rights":["Copyright 2012 Dan Lior"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/42374","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["McCarthy, Randy","Ando, Matthew","Rezk, Charles","Nevins, Thomas A."]},{"key":"dc:creator","label":"Author","values":["Lior, Dan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-02-03T19:36:43Z","2012-12"]},{"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":["Goodwillie","Functor Calculus","Taylor Tower","Robinson Bicomplex","Discrete Module","Discrete Functor"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2012 Dan Lior"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/42374"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Let $P_m$ and $D_m$ be the $m^{th}$ level and layer of the Goodwillie-Taylor tower for discrete modules. In \\cite{intermont_johnson_mccarthy08} the rank filtration of $D_1F$ is described and the associated spectral sequence is shown to be equivalent to the filtration by rows of the reduced Robinson bicomplex of $F$. We consider the rank filtrations of $P_mF$ and $D_mF$ and give explicit descriptions of the entries of the $E^1$ page of the associated spectral sequences. In the case $m=1$ these entries agree with those of the spectral sequence associated with the reduced Robinson bicomplex.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-08-13T21:01:04Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Lior_Dan.tex: 120093 bytes, checksum: 6b8b63e4d91fe6ab1ce2ddb51ec15b57 (MD5) Lior_Dan.pdf: 740808 bytes, checksum: d4dfb2d4ccbca76b0f31b53d4c47842f (MD5)","Made available in DSpace on 2013-02-03T19:36:43Z (GMT). No. of bitstreams: 3 Dan_Lior.pdf: 740808 bytes, checksum: d4dfb2d4ccbca76b0f31b53d4c47842f (MD5) Lior_Dan.tex: 120093 bytes, checksum: 6b8b63e4d91fe6ab1ce2ddb51ec15b57 (MD5) license.txt: 4058 bytes, checksum: 29c0f36057fc16324b4849bcdd37c6de (MD5)"]},{"key":"dc:title","label":"Title","values":["Computing the Goodwillie-Taylor tower of discrete modules"]}]}],"canonical_facts":{"dc:contributor":["McCarthy, Randy","Ando, Matthew","Rezk, Charles","Nevins, Thomas A."],"dc:creator":["Lior, Dan"],"dc:date":["2013-02-03T19:36:43Z","2012-12"],"dc:description":["Let $P_m$ and $D_m$ be the $m^{th}$ level and layer of the Goodwillie-Taylor tower for discrete modules. In \\cite{intermont_johnson_mccarthy08} the rank filtration of $D_1F$ is described and the associated spectral sequence is shown to be equivalent to the filtration by rows of the reduced Robinson bicomplex of $F$. We consider the rank filtrations of $P_mF$ and $D_mF$ and give explicit descriptions of the entries of the $E^1$ page of the associated spectral sequences. In the case $m=1$ these entries agree with those of the spectral sequence associated with the reduced Robinson bicomplex.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-08-13T21:01:04Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Lior_Dan.tex: 120093 bytes, checksum: 6b8b63e4d91fe6ab1ce2ddb51ec15b57 (MD5) Lior_Dan.pdf: 740808 bytes, checksum: d4dfb2d4ccbca76b0f31b53d4c47842f (MD5)","Made available in DSpace on 2013-02-03T19:36:43Z (GMT). No. of bitstreams: 3 Dan_Lior.pdf: 740808 bytes, checksum: d4dfb2d4ccbca76b0f31b53d4c47842f (MD5) Lior_Dan.tex: 120093 bytes, checksum: 6b8b63e4d91fe6ab1ce2ddb51ec15b57 (MD5) license.txt: 4058 bytes, checksum: 29c0f36057fc16324b4849bcdd37c6de (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/42374"],"dc:language":["en"],"dc:rights":["Copyright 2012 Dan Lior"],"dc:subject":["Goodwillie","Functor Calculus","Taylor Tower","Robinson Bicomplex","Discrete Module","Discrete Functor"],"dc:title":["Computing the Goodwillie-Taylor tower of discrete modules"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:33Z"}