{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22924"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22924","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A homotopy reciprocity law for ribbon disc complements","abstract":"In this paper, we present two new spines for ribbon disc complements. We describe Craggs's 3-dimensional spine and introduce a 2-dimensional spine ${\\cal W}\\sp2$ which we show satisfies the homotopy reciprocity law. We demonstrate that the reciprocity property remains invariant under insertions and conjecture that the property is invariant under deletions. If this is the case, then the ribbon disc complement spines described here satisfy the reciprocity law and, hence, are Kervaire.","abstract_html":"In this paper, we present two new spines for ribbon disc complements. We describe Craggs's 3-dimensional spine and introduce a 2-dimensional spine ${\\cal W}\\sp2$ which we show satisfies the homotopy reciprocity law. We demonstrate that the reciprocity property remains invariant under insertions and conjecture that the property is invariant under deletions. If this is the case, then the ribbon disc complement spines described here satisfy the reciprocity law and, hence, are Kervaire.","abstract_has_math":true,"creators":["Cavagnaro, Catherine Elizabeth"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Craggs, Robert F."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"10000-01-01","date_published":"10000-01-01","updated_at":"2026-07-22T22:25:20Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1995 Cavagnaro, Catherine Elizabeth"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624302","(UMI)AAI9624302"],"render_values":[{"text":"AAI9624302","href":null,"code":true},{"text":"(UMI)AAI9624302","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22924","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Craggs, Robert F."]},{"key":"dc:creator","label":"Author","values":["Cavagnaro, Catherine Elizabeth"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["10000-01-01","2011-05-07T13:56:01Z","1995"]},{"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"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Cavagnaro, Catherine Elizabeth"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624302","(UMI)AAI9624302","http://hdl.handle.net/2142/22924"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this paper, we present two new spines for ribbon disc complements. We describe Craggs's 3-dimensional spine and introduce a 2-dimensional spine ${\\cal W}\\sp2$ which we show satisfies the homotopy reciprocity law. We demonstrate that the reciprocity property remains invariant under insertions and conjecture that the property is invariant under deletions. If this is the case, then the ribbon disc complement spines described here satisfy the reciprocity law and, hence, are Kervaire.","Made available in DSpace on 2011-05-07T13:56:01Z (GMT). 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We describe Craggs's 3-dimensional spine and introduce a 2-dimensional spine ${\\cal W}\\sp2$ which we show satisfies the homotopy reciprocity law. We demonstrate that the reciprocity property remains invariant under insertions and conjecture that the property is invariant under deletions. If this is the case, then the ribbon disc complement spines described here satisfy the reciprocity law and, hence, are Kervaire.","Made available in DSpace on 2011-05-07T13:56:01Z (GMT). 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