{"id":"https://openalex.org/W7212255209","doi":"https://doi.org/10.48550/arxiv.2609.11074","title":"On the II$_{1}$ Factors of Fuchsian Groups","display_name":"On the II$_{1}$ Factors of Fuchsian Groups","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212255209","doi":"https://doi.org/10.48550/arxiv.2609.11074"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11074","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11074","pdf_url":"https://arxiv.org/pdf/2609.11074","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/2609.11074","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151321771","display_name":"D. Shlyakhtenko","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shlyakhtenko, D.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5151321771"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9980000257492065,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0005000000237487257,"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/T10849","display_name":"Finite Group Theory Research","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/von-neumann-algebras","display_name":"von Neumann algebras","score":0.8510000109672546},{"id":"https://openalex.org/keywords/free-group-factors","display_name":"free group factors","score":0.8130000233650208},{"id":"https://openalex.org/keywords/fundamental-group","display_name":"fundamental group","score":0.5950000286102295},{"id":"https://openalex.org/keywords/fuchsian-groups","display_name":"Fuchsian groups","score":0.9269999861717224},{"id":"https://openalex.org/keywords/free-independence","display_name":"free independence","score":0.6230000257492065},{"id":"https://openalex.org/keywords/psl-2-r","display_name":"PSL(2,R)","score":0.8989999890327454},{"id":"https://openalex.org/keywords/group-von-neumann-algebras","display_name":"group von Neumann algebras","score":0.6990000009536743}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8029999732971191},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6244000196456909},{"id":"https://openalex.org/C77021192","wikidata":"https://www.wikidata.org/wiki/Q431078","display_name":"Free group","level":3,"score":0.5321999788284302},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5202000141143799},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5156000256538391},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4984999895095825},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.48539999127388},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.40799999237060547},{"id":"https://openalex.org/C47527751","wikidata":"https://www.wikidata.org/wiki/Q1454165","display_name":"Free product","level":3,"score":0.39570000767707825},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38179999589920044},{"id":"https://openalex.org/C95627345","wikidata":"https://www.wikidata.org/wiki/Q1138961","display_name":"Quotient group","level":4,"score":0.3747999966144562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35429999232292175},{"id":"https://openalex.org/C46467970","wikidata":"https://www.wikidata.org/wiki/Q1361055","display_name":"Discrete group","level":3,"score":0.34060001373291016},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C130805567","wikidata":"https://www.wikidata.org/wiki/Q1162676","display_name":"Haar measure","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.30000001192092896},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.29919999837875366},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27399998903274536},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C196278274","wikidata":"https://www.wikidata.org/wiki/Q3845212","display_name":"Mapping class group","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C194674032","wikidata":"https://www.wikidata.org/wiki/Q1142190","display_name":"Skein","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11074","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11074","pdf_url":"https://arxiv.org/pdf/2609.11074","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.2609.11074","doi":"https://doi.org/10.48550/arxiv.2609.11074","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11074","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.11074","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11074","pdf_url":"https://arxiv.org/pdf/2609.11074","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/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212255209.pdf","grobid_xml":"https://content.openalex.org/works/W7212255209.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3153423235","https://openalex.org/W4322716997"],"related_works":["https://openalex.org/W7100351321","https://openalex.org/W654345825","https://openalex.org/W2159315270","https://openalex.org/W7098693323","https://openalex.org/W2093016720","https://openalex.org/W4242245669","https://openalex.org/W2511920385","https://openalex.org/W2034075419","https://openalex.org/W1511718135","https://openalex.org/W7095485262"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,29,53,65],"von":[3],"Neumann":[4],"algebras":[5],"of":[6,9,13,33,86],"fundamental":[7],"groups":[8],"closed":[10],"orientable":[11],"surfaces":[12],"genus":[14],"$g\\geq2$":[15],"are":[16],"free":[17,35,80],"group":[18,36,44,81],"factors":[19],"on":[20],"$2g-1$generators.":[21],"The":[22],"key":[23],"technical":[24],"ingredient":[25],"involves":[26],"a":[27,79,84],"proof":[28],"the":[30,34,43],"element":[31],"$w=ABA^{-1}B^{-1}$":[32],"$\\mathbb{F}_{2}=\\langle":[37],"A,B\\rangle$":[38],"is":[39,54,78],"freely":[40,55],"complemented":[41],"in":[42],"factor:":[45],"$L(\\mathbb{F}_{2})=W^{*}(w)*W^{*}(v)$":[46],"for":[47,66],"some":[48],"Haar":[49],"unitary":[50],"$v\\in":[51],"L(\\mathbb{F}_{2})$":[52],"independent":[56],"from":[57],"$w$.":[58],"Combined":[59],"with":[60],"previous":[61],"results,":[62],"we":[63],"conclude":[64],"an":[67],"arbitrary":[68],"finitely":[69],"generated":[70],"torsion-free":[71],"non-elementary":[72],"discrete":[73],"subgroup":[74],"$\u0393\\subset":[75],"PSL_{2}(\\mathbb{R})$,":[76],"$L(\u0393)$":[77],"factor,":[82],"settling":[83],"conjecture":[85],"de":[87],"la":[88],"Harpe":[89],"and":[90],"Voiculescu.":[91],"This":[92],"result":[93],"was":[94],"obtained":[95],"using":[96],"OpenAI's":[97],"ChatGPT":[98],"Pro":[99],"6.0.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}