{"id":"https://openalex.org/W7213320511","doi":"https://doi.org/10.48550/arxiv.2609.15733","title":"Algebraic and measurable embeddings between square-free right-angled Artin groups","display_name":"Algebraic and measurable embeddings between square-free right-angled Artin groups","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213320511","doi":"https://doi.org/10.48550/arxiv.2609.15733"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15733","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15733","pdf_url":"https://arxiv.org/pdf/2609.15733","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":"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/2609.15733","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114338336","display_name":"Adrien Abgrall","orcid":"https://orcid.org/0009-0008-1055-7917","observed_orcids":["https://orcid.org/0009-0008-1055-7917"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abgrall, Adrien","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151854833","display_name":"Alexandra Gurieva","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gurieva, Alexandra","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5053072261","display_name":"Camille Horbez","orcid":"https://orcid.org/0000-0003-1933-445X","observed_orcids":["https://orcid.org/0000-0003-1933-445X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Horbez, Camille","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9951000213623047,"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":0.9951000213623047,"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":0.0012000000569969416,"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"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/right-angled-artin-groups","display_name":"right-angled Artin groups","score":0.9980000257492065},{"id":"https://openalex.org/keywords/cohomological-dimension","display_name":"cohomological dimension","score":0.7239999771118164},{"id":"https://openalex.org/keywords/parabolic-subgroups","display_name":"parabolic subgroups","score":0.7649999856948853},{"id":"https://openalex.org/keywords/subgroup-generation","display_name":"subgroup generation","score":0.5879999995231628},{"id":"https://openalex.org/keywords/simplicial-graphs","display_name":"simplicial graphs","score":0.7070000171661377}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8809000253677368},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5701000094413757},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5633999705314636},{"id":"https://openalex.org/C201064014","wikidata":"https://www.wikidata.org/wiki/Q3956993","display_name":"Artin group","level":3,"score":0.5109999775886536},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4449999928474426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4392000138759613},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.43860000371932983},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42829999327659607},{"id":"https://openalex.org/C2778332477","wikidata":"https://www.wikidata.org/wiki/Q5141396","display_name":"Cohomological dimension","level":3,"score":0.423799991607666},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35659998655319214},{"id":"https://openalex.org/C75066664","wikidata":"https://www.wikidata.org/wiki/Q291126","display_name":"Semidirect product","level":3,"score":0.35370001196861267},{"id":"https://openalex.org/C47527751","wikidata":"https://www.wikidata.org/wiki/Q1454165","display_name":"Free product","level":3,"score":0.3474999964237213},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C105515060","wikidata":"https://www.wikidata.org/wiki/Q743179","display_name":"Normal subgroup","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C176637632","wikidata":"https://www.wikidata.org/wiki/Q2993300","display_name":"Artin L-function","level":3,"score":0.2815000116825104},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C127641909","wikidata":"https://www.wikidata.org/wiki/Q1457165","display_name":"Frobenius group","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.2703000009059906},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C2985491264","wikidata":"https://www.wikidata.org/wiki/Q761631","display_name":"Clique number","level":3,"score":0.2606000006198883},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C14669601","wikidata":"https://www.wikidata.org/wiki/Q2293759","display_name":"Torsion subgroup","level":4,"score":0.2524999976158142}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.15733","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15733","pdf_url":"https://arxiv.org/pdf/2609.15733","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05842967v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05842967","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.15733","doi":"https://doi.org/10.48550/arxiv.2609.15733","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15733","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:2609.15733","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15733","pdf_url":"https://arxiv.org/pdf/2609.15733","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213320511.pdf","grobid_xml":"https://content.openalex.org/works/W7213320511.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W3135353140","https://openalex.org/W4365211586","https://openalex.org/W4390784149","https://openalex.org/W7161054227","https://openalex.org/W7161142506"],"related_works":["https://openalex.org/W4365211586","https://openalex.org/W2735735223","https://openalex.org/W3206076766","https://openalex.org/W2060029831","https://openalex.org/W2936027061","https://openalex.org/W2582819232","https://openalex.org/W3020125943","https://openalex.org/W2762239436","https://openalex.org/W7161142506","https://openalex.org/W1025019368"],"abstract_inverted_index":{"Let":[0,103],"$\u0393,\u0394$":[1],"be":[2,54,105,120],"finite":[3],"simplicial":[4],"graphs,":[5],"and":[6,27,60,68,85,117,149],"assume":[7],"that":[8,16,78,147],"$\u0393$":[9],"has":[10,48],"no":[11],"induced":[12],"squares.":[13],"We":[14],"prove":[15],"the":[17,99,113,130,143,174,182],"right-angled":[18,139],"Artin":[19,140],"group":[20],"$A(\u0394)$":[21,30,61,79],"measurably":[22,80],"embeds":[23,31,81,89],"into":[24,82],"$A(\u0393)$":[25,59,69,83,123,133],"if":[26,29,84,87,152],"only":[28,86,144],"as":[32,90],"a":[33,36,49,91,106,138,158],"subgroup":[34,92,131],"in":[35,46,93,112,157,173],"graph":[37,115,176],"product":[38],"of":[39,108,122,132,160],"free":[40],"abelian":[41],"groups":[42],"over":[43],"$\u0393$.":[44,161],"This":[45],"turn":[47],"graph-theoretical":[50],"characterisation":[51],"which":[52],"can":[53],"checked":[55],"algorithmically.":[56],"If":[57],"additionally":[58],"have":[62],"cohomological":[63],"dimension":[64],"equal":[65],"to":[66,73,179],"two":[67],"is":[70,137,155],"not":[71],"isomorphic":[72],"$\\mathbb{Z}\\times":[74],"F_n$,":[75],"we":[76],"get":[77],"it":[88],"$A(\u0393)$.":[94],"Our":[95],"proof":[96],"relies":[97],"on":[98],"following":[100],"algebraic":[101],"statement.":[102],"$K_1,\\dots,K_n$":[104,172],"family":[107],"pairwise":[109,169],"disjoint":[110,170],"cliques":[111,171],"square-free":[114],"$\u0393$,":[116],"let":[118],"$g_1,\\dots,g_n$":[119,136],"elements":[121,183],"with":[124],"respective":[125],"parabolic":[126],"supports":[127],"$A(K_1),\\dots,A(K_n)$.":[128],"Then":[129],"generated":[134],"by":[135,185],"group,":[141],"where":[142],"relations":[145],"impose":[146],"$g_i$":[148,184],"$g_j$":[150],"commute":[151],"$K_i\\cup":[153],"K_j$":[154],"contained":[156],"clique":[159],"The":[162],"same":[163],"holds":[164],"true":[165],"more":[166],"generally":[167],"for":[168],"extension":[175],"$\u0393^{\\mathrm{ext}}$,":[177],"up":[178],"possibly":[180],"replacing":[181],"powers.":[186]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-16T00:00:00"}