{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/32655"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/32655","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Constructing Bitwisted Face Pairing 3-Manifolds","abstract":"The bitwist construction, originally discovered by Cannon, Floyd, and Parry, gives us a new method for finding face pairing descriptions of 3-manifolds. In this paper, I will describe the construction in a way suitable for a more general audience than the original research papers. Along the way, I will describe Dehn Surgery and a set of moves which allows us to change the framings of a link without changing the topology of the manifold obtained by Dehn Surgery. Once the theory has been developed, I will apply it to find several bitwist representations of the Poincaré Sphere and 3-Torus. Finally, I discuss how one might attempt to find a set of moves that can take one bitwist representation of a manifold to any other bitwist representation of the same manifold.","abstract_html":"The bitwist construction, originally discovered by Cannon, Floyd, and Parry, gives us a new method for finding face pairing descriptions of 3-manifolds. In this paper, I will describe the construction in a way suitable for a more general audience than the original research papers. Along the way, I will describe Dehn Surgery and a set of moves which allows us to change the framings of a link without changing the topology of the manifold obtained by Dehn Surgery. Once the theory has been developed, I will apply it to find several bitwist representations of the Poincaré Sphere and 3-Torus. Finally, I discuss how one might attempt to find a set of moves that can take one bitwist representation of a manifold to any other bitwist representation of the same manifold.","abstract_has_math":false,"creators":["Ackermann, Robert James"],"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":["Thomson, James E.","Brown, Ezra A."],"year":2008,"date_issued":"2008-04-29","date_published":"2008-04-29","updated_at":"2026-07-22T22:19:44Z","subjects":["Bitwisted 3-manifolds","Twisted 3-manifolds","Dehn Surgery","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":["etd-05122008-202129"],"render_values":[{"text":"etd-05122008-202129","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/32655","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":["Thomson, James E.","Brown, Ezra A."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Ackermann, Robert James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:36:29Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:36:29Z","2008-06-06"]},{"key":"dc:date.issued","label":"Date","values":["2008-04-29"]},{"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":["Bitwisted 3-manifolds","Twisted 3-manifolds","Dehn Surgery","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":["etd-05122008-202129"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/32655"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The bitwist construction, originally discovered by Cannon, Floyd, and Parry, gives us a new method for finding face pairing descriptions of 3-manifolds. In this paper, I will describe the construction in a way suitable for a more general audience than the original research papers. Along the way, I will describe Dehn Surgery and a set of moves which allows us to change the framings of a link without changing the topology of the manifold obtained by Dehn Surgery. Once the theory has been developed, I will apply it to find several bitwist representations of the Poincaré Sphere and 3-Torus. Finally, I discuss how one might attempt to find a set of moves that can take one bitwist representation of a manifold to any other bitwist representation of the same manifold."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Constructing Bitwisted Face Pairing 3-Manifolds"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Floyd, William J."],"dc:contributor.committeemember":["Thomson, James E.","Brown, Ezra A."],"dc:contributor.department":["Mathematics"],"dc:creator":["Ackermann, Robert James"],"dc:date.accessioned":["2014-03-14T20:36:29Z"],"dc:date.available":["2014-03-14T20:36:29Z","2008-06-06"],"dc:date.issued":["2008-04-29"],"dc:description.abstract":["The bitwist construction, originally discovered by Cannon, Floyd, and Parry, gives us a new method for finding face pairing descriptions of 3-manifolds. In this paper, I will describe the construction in a way suitable for a more general audience than the original research papers. Along the way, I will describe Dehn Surgery and a set of moves which allows us to change the framings of a link without changing the topology of the manifold obtained by Dehn Surgery. Once the theory has been developed, I will apply it to find several bitwist representations of the Poincaré Sphere and 3-Torus. 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