{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:soar.wichita.edu:10057/55544"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:soar.wichita.edu:10057/55544","repository":{"repo_id":"wichita-thes","name":"Wichita State University","base_url":"https://soar.wichita.edu/oai/request"},"display":{"title":"Positive curvature and discrete Abelian group actions","abstract":"In this thesis, we consider results due to Fang and Rong, and to Kennard, Khalili Samani, and Searle. We generalize two results of Fang and Rong to odd-dimensional, non-simply connected manifolds, replacing their assumption on how large the prime $p$ is with the assumption that the $\\mathbb{Z}$p-torus action has a fixed point. We also improve the lower bound on the rank of a $\\mathbb{Z}_2$-torus acting on a closed, positively curved Riemannian manifold $M_n$ with a fixed point in a result of Kennard, Khalili Samani, and Searle from (n + 1)/2 to approximately 2n/5, obtaining the same conclusion.","abstract_html":"In this thesis, we consider results due to Fang and Rong, and to Kennard, Khalili Samani, and Searle. We generalize two results of Fang and Rong to odd-dimensional, non-simply connected manifolds, replacing their assumption on how large the prime $p$ is with the assumption that the $\\mathbb{Z}$p-torus action has a fixed point. We also improve the lower bound on the rank of a <span class=\"etd-inline-math\">\\mathbb{Z}<sub>2</sub></span>-torus acting on a closed, positively curved Riemannian manifold <span class=\"etd-inline-math\">M<sub>n</sub></span> with a fixed point in a result of Kennard, Khalili Samani, and Searle from (n + 1)/2 to approximately 2n/5, obtaining the same conclusion.","abstract_has_math":true,"creators":["Ghazawneh, Farida"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-12","date_published":"2025-12","updated_at":"2026-07-24T06:05:48Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/55544"],"render_values":[{"text":"hdl:10057/55544","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2025-12"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/55544"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["In this thesis, we consider results due to Fang and Rong, and to Kennard, Khalili Samani, and Searle. We generalize two results of Fang and Rong to odd-dimensional, non-simply connected manifolds, replacing their assumption on how large the prime $p$ is with the assumption that the $\\mathbb{Z}$p-torus action has a fixed point. We also improve the lower bound on the rank of a $\\mathbb{Z}_2$-torus acting on a closed, positively curved Riemannian manifold $M_n$ with a fixed point in a result of Kennard, Khalili Samani, and Searle from (n + 1)/2 to approximately 2n/5, obtaining the same conclusion."]},{"key":"dc:title","label":"Title","values":["Positive curvature and discrete Abelian group actions"]}]}],"canonical_facts":{"dc:date.issued":["2025-12"],"dc:description.other":["In this thesis, we consider results due to Fang and Rong, and to Kennard, Khalili Samani, and Searle. We generalize two results of Fang and Rong to odd-dimensional, non-simply connected manifolds, replacing their assumption on how large the prime $p$ is with the assumption that the $\\mathbb{Z}$p-torus action has a fixed point. We also improve the lower bound on the rank of a $\\mathbb{Z}_2$-torus acting on a closed, positively curved Riemannian manifold $M_n$ with a fixed point in a result of Kennard, Khalili Samani, and Searle from (n + 1)/2 to approximately 2n/5, obtaining the same conclusion."],"dc:identifier":["hdl:10057/55544"],"dc:title":["Positive curvature and discrete Abelian group actions"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T06:05:48Z"}