{"id":{"repo_id":"temple","oai_identifier":"oai:scholarshare.temple.edu:20.500.12613/602"},"canonical_url":"https://search.dev.ndltd.org/etd/temple/oai:scholarshare.temple.edu:20.500.12613/602","repository":{"repo_id":"temple","name":"Temple University","base_url":"https://scholarshare.temple.edu/server/oai/request"},"display":{"title":"Veering Triangulations: Theory and Experiment","abstract":"Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. In the first part of this work, we obtain experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. Among other things, our experimental results strongly suggest that typical veering triangulations are non-geometric, i.e., they cannot be realized as a union of isometrically embedded hyperbolic tetrahedra. In the second part, we prove that veering triangulations are in fact generically non-geometric.","abstract_html":"Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. In the first part of this work, we obtain experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. Among other things, our experimental results strongly suggest that typical veering triangulations are non-geometric, i.e., they cannot be realized as a union of isometrically embedded hyperbolic tetrahedra. In the second part, we prove that veering triangulations are in fact generically non-geometric.","abstract_has_math":false,"creators":["Worden, William"],"institution":"Temple University. Libraries","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Futer, David"],"committee_chairs":[],"committee_members":["Stover, Matthew","Taylor, Samuel J.","Champanerkar, Abhijit, 1975-"],"year":2018,"date_issued":"2018","date_published":"2018","updated_at":"2026-07-27T21:22:02Z","subjects":["Mathematics","Fibered","Geometry","Hyperbolic","Topology","Triangulation","Veering"],"languages":["eng"],"rights":["IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available."],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/20.500.12613/602","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Futer, David"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Stover, Matthew","Taylor, Samuel J.","Champanerkar, Abhijit, 1975-"]},{"key":"dc:creator","label":"Author","values":["Worden, William"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-10-19T16:13:12Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-10-19T16:13:12Z"]},{"key":"dc:date.issued","label":"Date","values":["2018"]},{"key":"dc:publisher","label":"Institution","values":["Temple University. 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Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/20.500.12613/602"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Accompanied by two .py files. A Python interpreter is required to run a PY script in Windows."]},{"key":"dc:description.abstract","label":"Abstract","values":["Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. In the first part of this work, we obtain experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. Among other things, our experimental results strongly suggest that typical veering triangulations are non-geometric, i.e., they cannot be realized as a union of isometrically embedded hyperbolic tetrahedra. In the second part, we prove that veering triangulations are in fact generically non-geometric."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Veering Triangulations: Theory and Experiment"]}]}],"canonical_facts":{"dc:contributor.advisor":["Futer, David"],"dc:contributor.committeemember":["Stover, Matthew","Taylor, Samuel J.","Champanerkar, Abhijit, 1975-"],"dc:creator":["Worden, William"],"dc:date.accessioned":["2020-10-19T16:13:12Z"],"dc:date.available":["2020-10-19T16:13:12Z"],"dc:date.issued":["2018"],"dc:description":["Accompanied by two .py files. A Python interpreter is required to run a PY script in Windows."],"dc:description.abstract":["Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. In the first part of this work, we obtain experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. Among other things, our experimental results strongly suggest that typical veering triangulations are non-geometric, i.e., they cannot be realized as a union of isometrically embedded hyperbolic tetrahedra. In the second part, we prove that veering triangulations are in fact generically non-geometric."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/20.500.12613/602"],"dc:language.iso":["eng"],"dc:publisher":["Temple University. Libraries"],"dc:rights":["IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. 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