We explicitly construct 10 families of bad 3-orbifolds, X , having the following property: given any bad 3-orbifold, O, it admits an embedded suborbifold X ∈ X such that after removing this member from O, and capping the resulting boundary, and then iterating this process finitely many times, you obtain a good 3-orbifold. Reversing this process gives us a procedure to obtain any possible bad 3-orbifold starting with a good 3-orbifold. Each member of X has 1 or 2 spherical boundary components and has underlying topological space S2 × I or (S2 × S1)\\B3.
","abstract_html":"<p>We explicitly construct 10 families of bad 3-orbifolds, X , having the following property: given any bad 3-orbifold, O, it admits an embedded suborbifold X ∈ X such that after removing this member from O, and capping the resulting boundary, and then iterating this process finitely many times, you obtain a good 3-orbifold. Reversing this process gives us a procedure to obtain any possible bad 3-orbifold starting with a good 3-orbifold. Each member of X has 1 or 2 spherical boundary components and has underlying topological space S2 × I or (S2 × S1)\\B3.</p>","abstract_has_math":false,"creators":["Lehman, Rachel Julie"],"institution":null,"degree_name":"Doctor of Philosophy in Mathematics (PhD)","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Goodman-Strauss, Chaim","Clay, Matthew"],"advisors":["Rieck, Yo’av"],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-05-01T07:00:00Z","date_published":"2020-05-01T07:00:00Z","updated_at":"2026-07-24T00:59:15Z","subjects":["Manifolds","Orbifolds","Topology","Geometry and Topology"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uark.edu/etd/3587","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Goodman-Strauss, Chaim","Clay, Matthew"]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Rieck, Yo’av"]},{"key":"dc:creator","label":"Author","values":["Lehman, Rachel Julie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-06-11T07:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy in Mathematics (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Manifolds","Orbifolds","Topology","Geometry and Topology"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uark.edu/etd/3587"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We explicitly construct 10 families of bad 3-orbifolds, X , having the following property: given any bad 3-orbifold, O, it admits an embedded suborbifold X ∈ X such that after removing this member from O, and capping the resulting boundary, and then iterating this process finitely many times, you obtain a good 3-orbifold. Reversing this process gives us a procedure to obtain any possible bad 3-orbifold starting with a good 3-orbifold. Each member of X has 1 or 2 spherical boundary components and has underlying topological space S2 × I or (S2 × S1)\\B3.
"]},{"key":"dc:title","label":"Title","values":["A Structure Theorem for Bad 3-Orbifolds"]}]}],"canonical_facts":{"dc:contributor":["Goodman-Strauss, Chaim","Clay, Matthew"],"dc:contributor.advisor":["Rieck, Yo’av"],"dc:creator":["Lehman, Rachel Julie"],"dc:date":["2020"],"dc:date.available":["2020-06-11T07:00:00Z"],"dc:description.abstract":["We explicitly construct 10 families of bad 3-orbifolds, X , having the following property: given any bad 3-orbifold, O, it admits an embedded suborbifold X ∈ X such that after removing this member from O, and capping the resulting boundary, and then iterating this process finitely many times, you obtain a good 3-orbifold. Reversing this process gives us a procedure to obtain any possible bad 3-orbifold starting with a good 3-orbifold. Each member of X has 1 or 2 spherical boundary components and has underlying topological space S2 × I or (S2 × S1)\\B3.
"],"dc:identifier":["https://scholarworks.uark.edu/etd/3587"],"dc:subject":["Manifolds","Orbifolds","Topology","Geometry and Topology"],"dc:title":["A Structure Theorem for Bad 3-Orbifolds"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy in Mathematics (PhD)"]},"updated_at":"2026-07-24T00:59:15Z"}