{"id":{"repo_id":"wayne-thes","oai_identifier":"oai:digitalcommons.wayne.edu:oa_dissertations-1469"},"canonical_url":"https://search.dev.ndltd.org/etd/wayne-thes/oai:digitalcommons.wayne.edu:oa_dissertations-1469","repository":{"repo_id":"wayne-thes","name":"Wayne State University","base_url":"https://digitalcommons.wayne.edu/do/oai/"},"display":{"title":"Stabilization and classification of poincare duality embeddings","abstract":"<p>We define a space E(K,X) of Poincare Duality embeddings and show that such spaces admit a highly connected stabilization map.</p> <p>This serves as a tool for classifying Poincare Duality embeddings in terms of the homotopy types of their complements. In</p> <p>particular, a Poincare embedding gives rise to a fiberwise duality</p> <p>map in the category of retractive spaces over X. We use this construction to obtain a highly connected classification map with target a moduli space of unstable complements for Poincare embeddings. As consequences, we obtain stabilization and classication results for</p> <p>smooth embeddings.</p>","abstract_html":"&lt;p&gt;We define a space E(K,X) of Poincare Duality embeddings and show that such spaces admit a highly connected stabilization map.&lt;/p&gt; &lt;p&gt;This serves as a tool for classifying Poincare Duality embeddings in terms of the homotopy types of their complements. In&lt;/p&gt; &lt;p&gt;particular, a Poincare embedding gives rise to a fiberwise duality&lt;/p&gt; &lt;p&gt;map in the category of retractive spaces over X. We use this construction to obtain a highly connected classification map with target a moduli space of unstable complements for Poincare embeddings. As consequences, we obtain stabilization and classication results for&lt;/p&gt; &lt;p&gt;smooth embeddings.&lt;/p&gt;","abstract_has_math":false,"creators":["Peter, John Whitson"],"institution":null,"degree_name":"Ph.D.","degree_level":"Open Access Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["John R. Klein"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01T08:00:00Z","date_published":"2012-01-01T08:00:00Z","updated_at":"2026-07-24T05:59:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wayne.edu/oa_dissertations/470","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["John R. Klein"]},{"key":"dc:creator","label":"Author","values":["Peter, John Whitson"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-05-24T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wayne.edu/oa_dissertations/470"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We define a space E(K,X) of Poincare Duality embeddings and show that such spaces admit a highly connected stabilization map.</p> <p>This serves as a tool for classifying Poincare Duality embeddings in terms of the homotopy types of their complements. In</p> <p>particular, a Poincare embedding gives rise to a fiberwise duality</p> <p>map in the category of retractive spaces over X. We use this construction to obtain a highly connected classification map with target a moduli space of unstable complements for Poincare embeddings. As consequences, we obtain stabilization and classication results for</p> <p>smooth embeddings.</p>"]},{"key":"dc:title","label":"Title","values":["Stabilization and classification of poincare duality embeddings"]}]}],"canonical_facts":{"dc:contributor":["John R. Klein"],"dc:creator":["Peter, John Whitson"],"dc:date.available":["2013-05-24T07:00:00Z"],"dc:description.abstract":["<p>We define a space E(K,X) of Poincare Duality embeddings and show that such spaces admit a highly connected stabilization map.</p> <p>This serves as a tool for classifying Poincare Duality embeddings in terms of the homotopy types of their complements. In</p> <p>particular, a Poincare embedding gives rise to a fiberwise duality</p> <p>map in the category of retractive spaces over X. We use this construction to obtain a highly connected classification map with target a moduli space of unstable complements for Poincare embeddings. As consequences, we obtain stabilization and classication results for</p> <p>smooth embeddings.</p>"],"dc:identifier":["https://digitalcommons.wayne.edu/oa_dissertations/470"],"dc:subject":["Mathematics"],"dc:title":["Stabilization and classification of poincare duality embeddings"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T05:59:04Z"}