{"id":"https://openalex.org/W7196932644","doi":"https://doi.org/10.48550/arxiv.2608.04462","title":"Modular fusion categories with trivial Torelli group actions","display_name":"Modular fusion categories with trivial Torelli group actions","publication_year":2026,"publication_date":"2026-08-05","ids":{"openalex":"https://openalex.org/W7196932644","doi":"https://doi.org/10.48550/arxiv.2608.04462"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.04462","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.04462","pdf_url":"https://arxiv.org/pdf/2608.04462","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/2608.04462","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5145404764","display_name":"Liang Chang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chang, Liang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036841153","display_name":"Siu\u2010Hung Ng","orcid":"https://orcid.org/0009-0006-6791-5776","observed_orcids":["https://orcid.org/0009-0006-6791-5776"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ng, Siu-Hung","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5124101049","display_name":"Yilong Wang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yilong","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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.6890000104904175,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.6890000104904175,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.2312999963760376,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.020999999716877937,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/torelli-group","display_name":"Torelli group","score":0.9430000185966492}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8151000142097473},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6236000061035156},{"id":"https://openalex.org/C158525013","wikidata":"https://www.wikidata.org/wiki/Q2593739","display_name":"Fusion","level":2,"score":0.5662999749183655},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5654000043869019},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5539000034332275},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5467000007629395},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5151000022888184},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.4259999990463257},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3903999924659729},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37770000100135803},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.37619999051094055},{"id":"https://openalex.org/C196278274","wikidata":"https://www.wikidata.org/wiki/Q3845212","display_name":"Mapping class group","level":3,"score":0.3617999851703644},{"id":"https://openalex.org/C181633103","wikidata":"https://www.wikidata.org/wiki/Q1834342","display_name":"Modular group","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C131715654","wikidata":"https://www.wikidata.org/wiki/Q288465","display_name":"Group action","level":3,"score":0.3400999903678894},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31139999628067017},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28060001134872437},{"id":"https://openalex.org/C119494637","wikidata":"https://www.wikidata.org/wiki/Q7249476","display_name":"Projective representation","level":3,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.04462","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.04462","pdf_url":"https://arxiv.org/pdf/2608.04462","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":"doi:10.48550/arxiv.2608.04462","doi":"https://doi.org/10.48550/arxiv.2608.04462","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.04462","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:2608.04462","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.04462","pdf_url":"https://arxiv.org/pdf/2608.04462","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":[{"id":"https://openalex.org/G3218341711","display_name":null,"funder_award_id":"12571041","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7196932644.pdf","grobid_xml":"https://content.openalex.org/works/W7196932644.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3172623762","https://openalex.org/W7220670495","https://openalex.org/W2795288474","https://openalex.org/W4362554482","https://openalex.org/W2315122920","https://openalex.org/W2799847020","https://openalex.org/W2971122521","https://openalex.org/W1808624962","https://openalex.org/W2980269572","https://openalex.org/W2972015460"],"abstract_inverted_index":{"In":[0],"this":[1,105],"paper,":[2],"we":[3,108],"study":[4],"modular":[5,60,82,114],"fusion":[6,61,83,115],"categories":[7,84,98,116],"whose":[8],"mapping":[9,52],"class":[10,53,142],"group":[11,43,54,90],"representations":[12,29],"are":[13,136],"trivial":[14,130],"on":[15,22],"the":[16,23,27,41,47,50,73,81,87,123],"Torelli":[17,42,89],"groups,":[18],"with":[19,58,99,117],"particular":[20],"emphasis":[21],"congruence":[24],"properties":[25],"of":[26,30,49,113,140],"resulting":[28],"$\\mathrm{Sp}(2g,":[31],"\\mathbb{Z})$.":[32],"We":[33,78],"prove":[34],"that,":[35],"for":[36,85],"any":[37],"$g":[38],"\\ge":[39],"3$,":[40],"is":[44,69,91,128,133],"contained":[45,92],"in":[46,76,93,96],"kernel":[48],"genus-$g$":[51],"representation":[55],"$\u03c1_g$":[56],"associated":[57],"a":[59,110],"category":[62],"$\\mathcal{C}$":[63,68],"if":[64,67],"and":[65,121],"only":[66],"pointed.":[70],"This":[71],"refines":[72],"corresponding":[74],"result":[75],"\\cite{MW25}.":[77],"also":[79],"characterize":[80],"which":[86],"genus-$2$":[88],"$\\ker":[94],"\u03c1_2$;":[95],"particular,":[97],"isotropic":[100,118,135],"adjoint":[101,119],"subcategories":[102],"belong":[103],"to":[104],"class.":[106],"Finally,":[107],"give":[109],"complete":[111],"classification":[112],"subcategories,":[120],"determine":[122],"groups":[124,139],"$G$":[125],"satisfying":[126],"$\\mathcal{Z}(\\mathrm{Vect}_G)$":[127],"2-Torelli":[129],"but":[131],"$\\mathcal{Z}(\\mathrm{Vect}_G)_{\\mathrm{ad}}$":[132],"not":[134],"precisely":[137],"2-Engel":[138],"nilpotent":[141],"3.":[143]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-07T00:00:00"}