{"id":"https://openalex.org/W7213367997","doi":"https://doi.org/10.48550/arxiv.2609.14598","title":"From veering triangulations to convergence actions and back again","display_name":"From veering triangulations to convergence actions and back again","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7213367997","doi":"https://doi.org/10.48550/arxiv.2609.14598"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14598","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14598","pdf_url":"https://arxiv.org/pdf/2609.14598","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.14598","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116659844","display_name":"Jason Fox Manning","orcid":"https://orcid.org/0000-0002-0143-7795","observed_orcids":["https://orcid.org/0000-0002-0143-7795"]},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Manning, Jason Fox","raw_affiliation_strings":["Department of Mathematics , Cornell University , Ithaca , New York , 14853 , United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Cornell University , Ithaca , New York , 14853 , United States","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052496150","display_name":"Saul Schleimer","orcid":"https://orcid.org/0000-0003-3362-7822","observed_orcids":["https://orcid.org/0000-0003-3362-7822"]},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Schleimer, Saul","raw_affiliation_strings":["Department of Mathematics , Cornell University , Ithaca , New York , 14853 , United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Cornell University , Ithaca , New York , 14853 , United States","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058246509","display_name":"Henry Segerman","orcid":"https://orcid.org/0000-0002-4532-3095","observed_orcids":["https://orcid.org/0000-0002-4532-3095"]},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Segerman, Henry","raw_affiliation_strings":["Department of Mathematics , Cornell University , Ithaca , New York , 14853 , United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Cornell University , Ithaca , New York , 14853 , United States","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cannon-thurston-maps","display_name":"Cannon-Thurston maps","score":0.9309999942779541},{"id":"https://openalex.org/keywords/surface-subgroups","display_name":"surface subgroups","score":0.7440000176429749},{"id":"https://openalex.org/keywords/fundamental-group-actions","display_name":"fundamental group actions","score":0.722000002861023}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.769599974155426},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7156999707221985},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.6965000033378601},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.6269000172615051},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6114000082015991},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5764999985694885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4047999978065491},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3131999969482422},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C167117609","wikidata":"https://www.wikidata.org/wiki/Q17078161","display_name":"Point set triangulation","level":3,"score":0.29030001163482666},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2766999900341034},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.266400009393692}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14598","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14598","pdf_url":"https://arxiv.org/pdf/2609.14598","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.14598","doi":"https://doi.org/10.48550/arxiv.2609.14598","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14598","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.14598","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14598","pdf_url":"https://arxiv.org/pdf/2609.14598","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1382440375","display_name":"Veering Triangulations and Visualization","funder_award_id":"2203993","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2397474635","display_name":"Three- and Four-Dimensional Triangulations and Mathematical Visualization","funder_award_id":"1708239","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2488694901","display_name":"Mathematical Sciences Research Institute (MSRI)","funder_award_id":"1928930","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2879864793","display_name":null,"funder_award_id":"UAR 839","funder_id":"https://openalex.org/F4320328291","funder_display_name":"Institut Henri Poincar\u00e9"},{"id":"https://openalex.org/G2919294553","display_name":"Institute for Computational and Experimental Research in Mathematics","funder_award_id":"1439786","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G329468232","display_name":null,"funder_award_id":"DMS-1928930","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G3375465512","display_name":null,"funder_award_id":"ANR-10-LABX-59-01","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"},{"id":"https://openalex.org/G4299339130","display_name":null,"funder_award_id":"1439786","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G4663222005","display_name":null,"funder_award_id":"1928930","funder_id":"https://openalex.org/F4320306151","funder_display_name":"Alfred P. Sloan Foundation"},{"id":"https://openalex.org/G4972001970","display_name":null,"funder_award_id":"DMS-1928930","funder_id":"https://openalex.org/F4320306151","funder_display_name":"Alfred P. Sloan Foundation"},{"id":"https://openalex.org/G5058101487","display_name":null,"funder_award_id":"ANR-10-LABX-59- 01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6019427330","display_name":null,"funder_award_id":"1928930","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G6363417690","display_name":null,"funder_award_id":"UAR 839 CNRS-Sorbonne Universit\u00e9","funder_id":"https://openalex.org/F4320328291","funder_display_name":"Institut Henri Poincar\u00e9"},{"id":"https://openalex.org/G6389258043","display_name":null,"funder_award_id":"UAR 839","funder_id":"https://openalex.org/F4320330232","funder_display_name":"Sorbonne Universit\u00e9"},{"id":"https://openalex.org/G6453481984","display_name":null,"funder_award_id":"10-LABX-59-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6505494016","display_name":null,"funder_award_id":"UAR 839 CNRS","funder_id":"https://openalex.org/F4320328291","funder_display_name":"Institut Henri Poincar\u00e9"},{"id":"https://openalex.org/G6758477442","display_name":null,"funder_award_id":"DMS\u20101439786","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G7048127755","display_name":null,"funder_award_id":"DMS-1928930","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7342182005","display_name":null,"funder_award_id":"ANR-10-LABX-59-01","funder_id":"https://openalex.org/F4320328291","funder_display_name":"Institut Henri Poincar\u00e9"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320320273","display_name":"University of Cambridge","ror":"https://ror.org/013meh722"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320328291","display_name":"Institut Henri Poincar\u00e9","ror":null},{"id":"https://openalex.org/F4320330232","display_name":"Sorbonne Universit\u00e9","ror":null},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213367997.pdf","grobid_xml":"https://content.openalex.org/works/W7213367997.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W120381637","https://openalex.org/W202435172","https://openalex.org/W1486462508","https://openalex.org/W1523420055","https://openalex.org/W1547457386","https://openalex.org/W1572014218","https://openalex.org/W1589886470","https://openalex.org/W1954822129","https://openalex.org/W1967057555","https://openalex.org/W1972545445","https://openalex.org/W1976449906","https://openalex.org/W2003111828","https://openalex.org/W2014843102","https://openalex.org/W2037070544","https://openalex.org/W2042359080","https://openalex.org/W2044720368","https://openalex.org/W2046984348","https://openalex.org/W2052099954","https://openalex.org/W2055527098","https://openalex.org/W2064521394","https://openalex.org/W2080671211","https://openalex.org/W2084633334","https://openalex.org/W2093177117","https://openalex.org/W2102521122","https://openalex.org/W2105766538","https://openalex.org/W2117667600","https://openalex.org/W2121805679","https://openalex.org/W2169194620","https://openalex.org/W2323546321","https://openalex.org/W2325779819","https://openalex.org/W2477208441","https://openalex.org/W2939088299","https://openalex.org/W3092530310","https://openalex.org/W3100107854","https://openalex.org/W3193658416","https://openalex.org/W4285781134","https://openalex.org/W4293865428","https://openalex.org/W4399863489","https://openalex.org/W4414694382","https://openalex.org/W6893942278","https://openalex.org/W7155497501","https://openalex.org/W7157059876","https://openalex.org/W7167736454"],"related_works":["https://openalex.org/W3100107854","https://openalex.org/W3134837255","https://openalex.org/W7101210812","https://openalex.org/W3039057607","https://openalex.org/W2761545364","https://openalex.org/W1972545445","https://openalex.org/W7214233004","https://openalex.org/W1555632387","https://openalex.org/W7168248133","https://openalex.org/W2986452021"],"abstract_inverted_index":{"Suppose":[0],"that":[1,17,43,85],"$M$":[2,25],"is":[3,30,47,69,79],"a":[4,11,31,37],"finite-volume":[5],"cusped":[6,100],"hyperbolic":[7,54],"three-manifold,":[8],"equipped":[9],"with":[10],"veering":[12,28,45,65],"triangulation":[13],"$\\mathcal{V}$.":[14],"We":[15],"prove":[16],"the":[18,21,27,44,51,73,94,99],"action":[19],"of":[20,24,39,53,110],"fundamental":[22],"group":[23],"on":[26],"two-sphere":[29,46],"geometrically":[32],"finite":[33],"convergence":[34],"action.":[35],"Applying":[36],"result":[38],"Yaman,":[40],"we":[41,59,71,81,103],"deduce":[42],"equivariantly":[48],"homeomorphic":[49],"to":[50,64,107],"boundary":[52],"space.":[55],"As":[56],"an":[57,105],"application,":[58],"obtain":[60,82],"Cannon-Thurston":[61,75,83,112],"maps":[62,84],"associated":[63],"triangulations.":[66],"If":[67,77],"$\\mathcal{V}$":[68],"layered":[70],"recover":[72],"classical":[74],"map.":[76],"it":[78],"not":[80,87],"do":[86],"come":[88],"from":[89],"surface":[90],"subgroups.":[91],"These":[92],"are":[93],"first":[95],"such":[96],"examples":[97],"in":[98],"case.":[101],"Finally,":[102],"implement":[104],"algorithm":[106],"draw":[108],"approximations":[109,118],"these":[111],"maps.":[113],"This":[114],"improves":[115],"upon":[116],"previous":[117],"obtained":[119],"by":[120],"Thurston":[121],"and":[122],"others.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}