{"id":{"repo_id":"cornell","oai_identifier":"oai:ecommons.cornell.edu:1813/31216"},"canonical_url":"https://search.dev.ndltd.org/etd/cornell/oai:ecommons.cornell.edu:1813/31216","repository":{"repo_id":"cornell","name":"Cornell University","base_url":"https://ecommons.cornell.edu/server/oai/request"},"display":{"title":"Graphs Of Free Groups And Their Measure Equivalence.","abstract":"This work concerns the Geometric Group Theory of an interesting class of groups that can be obtained as graphs of free groups. These groups are called Quadratic Baumslag-Solitar groups, and are defined by graphs of groups that have infinite cyclic edge groups, and whose vertex groups are either infinite cyclic, or surface groups [pi]1 (S ) that are \"attached by their boundary\", meaning that the edge groups of the adjacent edges correspond to the subgroups generated by the boundary classes of S . More generally, we may also take S to be a 2-orbifold. The first part of the thesis studies JSJ decompositions for groups. We prove that, in most cases, the defining graph of groups of a Quadratic Baumslag-Solitar group is a JSJ decomposition in the sense of Rips and Sela [36]. This generalizes a result by Forester [11]. The second part studies measure equivalence between groups. It involves the concept of measure free factors of a group, which is a generalization of that of free factors, in a measure theoretic context. We find new families of cyclic measure free factors of free groups and some virtually free groups, following a question by D. Gaboriau [16]. Then we characterize the Quadratic Baumslag-Solitar groups that are measure equivalent to a free group, according to their defining graphs of groups.","abstract_html":"This work concerns the Geometric Group Theory of an interesting class of groups that can be obtained as graphs of free groups. These groups are called Quadratic Baumslag-Solitar groups, and are defined by graphs of groups that have infinite cyclic edge groups, and whose vertex groups are either infinite cyclic, or surface groups [pi]1 (S ) that are "attached by their boundary", meaning that the edge groups of the adjacent edges correspond to the subgroups generated by the boundary classes of S . More generally, we may also take S to be a 2-orbifold. The first part of the thesis studies JSJ decompositions for groups. We prove that, in most cases, the defining graph of groups of a Quadratic Baumslag-Solitar group is a JSJ decomposition in the sense of Rips and Sela [36]. This generalizes a result by Forester [11]. The second part studies measure equivalence between groups. It involves the concept of measure free factors of a group, which is a generalization of that of free factors, in a measure theoretic context. We find new families of cyclic measure free factors of free groups and some virtually free groups, following a question by D. Gaboriau [16]. Then we characterize the Quadratic Baumslag-Solitar groups that are measure equivalent to a free group, according to their defining graphs of groups.","abstract_has_math":false,"creators":["Alonso, Juan"],"institution":"Cornell University","degree_name":"Ph. D., Mathematics","degree_level":"Doctor of Philosophy","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":["Moore, Justin Tatch","Brown, Kenneth Stephen"],"year":2012,"date_issued":"2012-08-20","date_published":"2012-08-20","updated_at":"2026-07-24T01:49:00Z","subjects":["JSJ decomposition","Measure equivalence","Measure free factor"],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1813/31216","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Moore, Justin Tatch","Brown, Kenneth Stephen"]},{"key":"dc:creator","label":"Author","values":["Alonso, Juan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-01-31T19:46:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-01-31T19:46:38Z"]},{"key":"dc:date.issued","label":"Date","values":["2012-08-20"]},{"key":"dc:type","label":"Dc Type","values":["dissertation or thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctor of Philosophy"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D., Mathematics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Cornell University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["JSJ decomposition","Measure equivalence","Measure free factor"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1813/31216"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This work concerns the Geometric Group Theory of an interesting class of groups that can be obtained as graphs of free groups. These groups are called Quadratic Baumslag-Solitar groups, and are defined by graphs of groups that have infinite cyclic edge groups, and whose vertex groups are either infinite cyclic, or surface groups [pi]1 (S ) that are \"attached by their boundary\", meaning that the edge groups of the adjacent edges correspond to the subgroups generated by the boundary classes of S . More generally, we may also take S to be a 2-orbifold. The first part of the thesis studies JSJ decompositions for groups. We prove that, in most cases, the defining graph of groups of a Quadratic Baumslag-Solitar group is a JSJ decomposition in the sense of Rips and Sela [36]. This generalizes a result by Forester [11]. The second part studies measure equivalence between groups. It involves the concept of measure free factors of a group, which is a generalization of that of free factors, in a measure theoretic context. We find new families of cyclic measure free factors of free groups and some virtually free groups, following a question by D. Gaboriau [16]. Then we characterize the Quadratic Baumslag-Solitar groups that are measure equivalent to a free group, according to their defining graphs of groups."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Graphs Of Free Groups And Their Measure Equivalence."]}]}],"canonical_facts":{"dc:contributor.committeemember":["Moore, Justin Tatch","Brown, Kenneth Stephen"],"dc:creator":["Alonso, Juan"],"dc:date.accessioned":["2013-01-31T19:46:38Z"],"dc:date.available":["2013-01-31T19:46:38Z"],"dc:date.issued":["2012-08-20"],"dc:description.abstract":["This work concerns the Geometric Group Theory of an interesting class of groups that can be obtained as graphs of free groups. These groups are called Quadratic Baumslag-Solitar groups, and are defined by graphs of groups that have infinite cyclic edge groups, and whose vertex groups are either infinite cyclic, or surface groups [pi]1 (S ) that are \"attached by their boundary\", meaning that the edge groups of the adjacent edges correspond to the subgroups generated by the boundary classes of S . More generally, we may also take S to be a 2-orbifold. The first part of the thesis studies JSJ decompositions for groups. We prove that, in most cases, the defining graph of groups of a Quadratic Baumslag-Solitar group is a JSJ decomposition in the sense of Rips and Sela [36]. This generalizes a result by Forester [11]. The second part studies measure equivalence between groups. It involves the concept of measure free factors of a group, which is a generalization of that of free factors, in a measure theoretic context. We find new families of cyclic measure free factors of free groups and some virtually free groups, following a question by D. Gaboriau [16]. Then we characterize the Quadratic Baumslag-Solitar groups that are measure equivalent to a free group, according to their defining graphs of groups."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/1813/31216"],"dc:language.iso":["en_US"],"dc:subject":["JSJ decomposition","Measure equivalence","Measure free factor"],"dc:title":["Graphs Of Free Groups And Their Measure Equivalence."],"dc:type":["dissertation or thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctor of Philosophy"],"thesis:degree_name":["Ph. D., Mathematics"],"thesis:institution_name":["Cornell University"]},"updated_at":"2026-07-24T01:49:00Z"}