{"id":{"repo_id":"temple","oai_identifier":"oai:scholarshare.temple.edu:20.500.12613/6910"},"canonical_url":"https://search.dev.ndltd.org/etd/temple/oai:scholarshare.temple.edu:20.500.12613/6910","repository":{"repo_id":"temple","name":"Temple University","base_url":"https://scholarshare.temple.edu/server/oai/request"},"display":{"title":"GT-shadows related to finite quotients of the full modular group","abstract":"GT-shadows are tantalizing objects that can be thought of as “approximations” to elements of the mysterious Grothendieck-Teichmueller group GT introduced by V. Drinfeld in 1990 [5]. GT-shadows [4] form a groupoid whose objects are certain finite index normal subgroups of Artin’s braid group B4 on 4 strands. In this thesis we introduce GT-shadows for the gentle version GTgen of the Grothendieck-Teichmueller group. These entities are morphisms of a groupoid GTSh whose objects are certain finite index normal subgroups of Artin’s braid group B3 on 3 strands. We explore the connected components of GTSh for sub- groups of B3 coming from the standard homomorphism from B3 to SL2(Z/qZ), where q is a power of an odd prime integer > 3.","abstract_html":"GT-shadows are tantalizing objects that can be thought of as “approximations” to elements of the mysterious Grothendieck-Teichmueller group GT introduced by V. Drinfeld in 1990 [5]. GT-shadows [4] form a groupoid whose objects are certain finite index normal subgroups of Artin’s braid group B4 on 4 strands. In this thesis we introduce GT-shadows for the gentle version GTgen of the Grothendieck-Teichmueller group. These entities are morphisms of a groupoid GTSh whose objects are certain finite index normal subgroups of Artin’s braid group B3 on 3 strands. We explore the connected components of GTSh for sub- groups of B3 coming from the standard homomorphism from B3 to SL2(Z/qZ), where q is a power of an odd prime integer > 3.","abstract_has_math":false,"creators":["Xia, Jingfeng"],"institution":"Temple University. Libraries","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Dolgushev, Vasily"],"committee_chairs":[],"committee_members":["Lorenz, Martin, 1951-","Stover, Matthew","Combe, Noémie"],"year":2021,"date_issued":"2021","date_published":"2021","updated_at":"2026-07-27T21:20:15Z","subjects":["Mathematics"],"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/20.500.12613/6910","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Dolgushev, Vasily"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Lorenz, Martin, 1951-","Stover, Matthew","Combe, Noémie"]},{"key":"dc:creator","label":"Author","values":["Xia, Jingfeng"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-08-23T18:22:58Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-08-23T18:22:58Z"]},{"key":"dc:date.issued","label":"Date","values":["2021"]},{"key":"dc:publisher","label":"Institution","values":["Temple University. 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GT-shadows [4] form a groupoid whose objects are certain finite index normal subgroups of Artin’s braid group B4 on 4 strands. In this thesis we introduce GT-shadows for the gentle version GTgen of the Grothendieck-Teichmueller group. These entities are morphisms of a groupoid GTSh whose objects are certain finite index normal subgroups of Artin’s braid group B3 on 3 strands. We explore the connected components of GTSh for sub- groups of B3 coming from the standard homomorphism from B3 to SL2(Z/qZ), where q is a power of an odd prime integer > 3."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.S."]},{"key":"dc:title","label":"Title","values":["GT-shadows related to finite quotients of the full modular group"]}]}],"canonical_facts":{"dc:contributor.advisor":["Dolgushev, Vasily"],"dc:contributor.committeemember":["Lorenz, Martin, 1951-","Stover, Matthew","Combe, Noémie"],"dc:creator":["Xia, Jingfeng"],"dc:date.accessioned":["2021-08-23T18:22:58Z"],"dc:date.available":["2021-08-23T18:22:58Z"],"dc:date.issued":["2021"],"dc:description.abstract":["GT-shadows are tantalizing objects that can be thought of as “approximations” to elements of the mysterious Grothendieck-Teichmueller group GT introduced by V. Drinfeld in 1990 [5]. GT-shadows [4] form a groupoid whose objects are certain finite index normal subgroups of Artin’s braid group B4 on 4 strands. In this thesis we introduce GT-shadows for the gentle version GTgen of the Grothendieck-Teichmueller group. These entities are morphisms of a groupoid GTSh whose objects are certain finite index normal subgroups of Artin’s braid group B3 on 3 strands. We explore the connected components of GTSh for sub- groups of B3 coming from the standard homomorphism from B3 to SL2(Z/qZ), where q is a power of an odd prime integer > 3."],"dc:description.degree":["M.S."],"dc:identifier.uri":["http://hdl.handle.net/20.500.12613/6910"],"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. 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."],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Mathematics"],"dc:title":["GT-shadows related to finite quotients of the full modular group"],"dc:type":["Text"]},"updated_at":"2026-07-27T21:20:15Z"}