{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/48188"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/48188","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Cycle-Free Twisted Face-Pairing 3-Manifolds","abstract":"In 2-dimensional topology, quotients of polygons by edge-pairings provide a rich source of examples of closed, connected, orientable surfaces. In fact, they provide all such examples. The 3-dimensional analogue of an edge-pairing of a polygon is a face-pairing of a faceted 3-ball. Unfortunately, quotients of faceted 3-balls by face-pairings rarely provide us with examples of 3-manifolds due to singularities that arise at the vertices. However, any face-pairing of a faceted 3-ball may be slighted modified so that its quotient is a genuine manifold, i.e. free of singularities. The modified face-pairing is called a twisted face-pairing. It is natural to ask which closed, connected, orientable 3-manifolds may be obtained as quotients of twisted face-pairings. In this paper, we focus on a special class of face-pairings called cycle-free twisted face-pairings and give description of their quotient spaces in terms of integer weighted graphs. We use this description to prove that most spherical 3-manifolds can be obtained as quotients of cycle-free twisted face-pairings, but the Poincaré homology 3-sphere cannot.","abstract_html":"In 2-dimensional topology, quotients of polygons by edge-pairings provide a rich source of examples of closed, connected, orientable surfaces. In fact, they provide all such examples. The 3-dimensional analogue of an edge-pairing of a polygon is a face-pairing of a faceted 3-ball. Unfortunately, quotients of faceted 3-balls by face-pairings rarely provide us with examples of 3-manifolds due to singularities that arise at the vertices. However, any face-pairing of a faceted 3-ball may be slighted modified so that its quotient is a genuine manifold, i.e. free of singularities. The modified face-pairing is called a twisted face-pairing. It is natural to ask which closed, connected, orientable 3-manifolds may be obtained as quotients of twisted face-pairings. In this paper, we focus on a special class of face-pairings called cycle-free twisted face-pairings and give description of their quotient spaces in terms of integer weighted graphs. We use this description to prove that most spherical 3-manifolds can be obtained as quotients of cycle-free twisted face-pairings, but the Poincaré homology 3-sphere cannot.","abstract_has_math":false,"creators":["Gartland, Christopher John"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Floyd, William J."],"committee_members":["Linnell, Peter A.","Haskell, Peter E."],"year":2014,"date_issued":"2014-05-29","date_published":"2014-05-29","updated_at":"2026-07-22T22:20:12Z","subjects":["3-manifolds","plumbing graphs","Seifert fibered spaces","face-pairings"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:3082"],"render_values":[{"text":"vt_gsexam:3082","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/48188","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Floyd, William J."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Linnell, Peter A.","Haskell, Peter E."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Gartland, Christopher John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-05-30T08:00:54Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-05-30T08:00:54Z"]},{"key":"dc:date.issued","label":"Date","values":["2014-05-29"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["3-manifolds","plumbing graphs","Seifert fibered spaces","face-pairings"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:3082"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/48188"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In 2-dimensional topology, quotients of polygons by edge-pairings provide a rich source of examples of closed, connected, orientable surfaces. In fact, they provide all such examples. The 3-dimensional analogue of an edge-pairing of a polygon is a face-pairing of a faceted 3-ball. Unfortunately, quotients of faceted 3-balls by face-pairings rarely provide us with examples of 3-manifolds due to singularities that arise at the vertices. However, any face-pairing of a faceted 3-ball may be slighted modified so that its quotient is a genuine manifold, i.e. free of singularities. The modified face-pairing is called a twisted face-pairing. It is natural to ask which closed, connected, orientable 3-manifolds may be obtained as quotients of twisted face-pairings. In this paper, we focus on a special class of face-pairings called cycle-free twisted face-pairings and give description of their quotient spaces in terms of integer weighted graphs. We use this description to prove that most spherical 3-manifolds can be obtained as quotients of cycle-free twisted face-pairings, but the Poincaré homology 3-sphere cannot."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Cycle-Free Twisted Face-Pairing 3-Manifolds"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Floyd, William J."],"dc:contributor.committeemember":["Linnell, Peter A.","Haskell, Peter E."],"dc:contributor.department":["Mathematics"],"dc:creator":["Gartland, Christopher John"],"dc:date.accessioned":["2014-05-30T08:00:54Z"],"dc:date.available":["2014-05-30T08:00:54Z"],"dc:date.issued":["2014-05-29"],"dc:description.abstract":["In 2-dimensional topology, quotients of polygons by edge-pairings provide a rich source of examples of closed, connected, orientable surfaces. In fact, they provide all such examples. The 3-dimensional analogue of an edge-pairing of a polygon is a face-pairing of a faceted 3-ball. Unfortunately, quotients of faceted 3-balls by face-pairings rarely provide us with examples of 3-manifolds due to singularities that arise at the vertices. However, any face-pairing of a faceted 3-ball may be slighted modified so that its quotient is a genuine manifold, i.e. free of singularities. The modified face-pairing is called a twisted face-pairing. It is natural to ask which closed, connected, orientable 3-manifolds may be obtained as quotients of twisted face-pairings. In this paper, we focus on a special class of face-pairings called cycle-free twisted face-pairings and give description of their quotient spaces in terms of integer weighted graphs. We use this description to prove that most spherical 3-manifolds can be obtained as quotients of cycle-free twisted face-pairings, but the Poincaré homology 3-sphere cannot."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:3082"],"dc:identifier.uri":["http://hdl.handle.net/10919/48188"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["3-manifolds","plumbing graphs","Seifert fibered spaces","face-pairings"],"dc:title":["Cycle-Free Twisted Face-Pairing 3-Manifolds"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:12Z"}