{"id":{"repo_id":"penn","oai_identifier":"oai:repository.upenn.edu:20.500.14332/31917"},"canonical_url":"https://search.dev.ndltd.org/etd/penn/oai:repository.upenn.edu:20.500.14332/31917","repository":{"repo_id":"penn","name":"University of Pennsylvania","base_url":"https://repository.upenn.edu/server/oai/request"},"display":{"title":"Derived Lie Infinity-Groupoids And Algebroids In Higher Differential Geometry","abstract":"We study various problems arising in higher geometry using derived Lie $\\infty$-groupoids and algebroids. We construct homotopical algebras for derived Lie $\\infty$-groupoids and algebroids and study their homotopy-coherent representations. Then we apply these tools in studying singular foliations and their characteristic classes. Finally, we prove an $A_{\\infty}$ de Rham theorem and higher Riemann-Hilbert correspondence for foliated manifolds.","abstract_html":"We study various problems arising in higher geometry using derived Lie $\\infty$-groupoids and algebroids. We construct homotopical algebras for derived Lie $\\infty$-groupoids and algebroids and study their homotopy-coherent representations. Then we apply these tools in studying singular foliations and their characteristic classes. Finally, we prove an <span class=\"etd-inline-math\">A<sub>\\infty</sub></span> de Rham theorem and higher Riemann-Hilbert correspondence for foliated manifolds.","abstract_has_math":true,"creators":["Zeng, Qingyun"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Jonathan Block"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021","date_published":"2021","updated_at":"2026-07-24T03:45:15Z","subjects":[],"languages":["en"],"rights":["Qingyun Zeng"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.upenn.edu/handle/20.500.14332/31917","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Jonathan Block"]},{"key":"dc:creator","label":"Author","values":["Zeng, Qingyun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05-18T03:29:06.000"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-05-22T18:29:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-01-31T00:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2021"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation/Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Qingyun Zeng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repository.upenn.edu/handle/20.500.14332/31917"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We study various problems arising in higher geometry using derived Lie $\\infty$-groupoids and algebroids. We construct homotopical algebras for derived Lie $\\infty$-groupoids and algebroids and study their homotopy-coherent representations. Then we apply these tools in studying singular foliations and their characteristic classes. Finally, we prove an $A_{\\infty}$ de Rham theorem and higher Riemann-Hilbert correspondence for foliated manifolds."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy (PhD)"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Derived Lie Infinity-Groupoids And Algebroids In Higher Differential Geometry"]}]}],"canonical_facts":{"dc:contributor.advisor":["Jonathan Block"],"dc:creator":["Zeng, Qingyun"],"dc:date":["2023-05-18T03:29:06.000"],"dc:date.accessioned":["2023-05-22T18:29:08Z"],"dc:date.available":["2025-01-31T00:00:00Z"],"dc:date.issued":["2021"],"dc:description.abstract":["We study various problems arising in higher geometry using derived Lie $\\infty$-groupoids and algebroids. We construct homotopical algebras for derived Lie $\\infty$-groupoids and algebroids and study their homotopy-coherent representations. Then we apply these tools in studying singular foliations and their characteristic classes. Finally, we prove an $A_{\\infty}$ de Rham theorem and higher Riemann-Hilbert correspondence for foliated manifolds."],"dc:description.degree":["Doctor of Philosophy (PhD)"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://repository.upenn.edu/handle/20.500.14332/31917"],"dc:language":["en"],"dc:rights":["Qingyun Zeng"],"dc:title":["Derived Lie Infinity-Groupoids And Algebroids In Higher Differential Geometry"],"dc:type":["Dissertation/Thesis"]},"updated_at":"2026-07-24T03:45:15Z"}