{"id":"https://openalex.org/W7213601897","doi":"https://doi.org/10.48550/arxiv.2609.19341","title":"The Drinfeld associator and $A_\\infty$ functors","display_name":"The Drinfeld associator and $A_\\infty$ functors","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213601897","doi":"https://doi.org/10.48550/arxiv.2609.19341"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.19341","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19341","pdf_url":"https://arxiv.org/pdf/2609.19341","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/2609.19341","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051537481","display_name":"Nikita Markarian","orcid":"https://orcid.org/0000-0002-2705-4776","observed_orcids":["https://orcid.org/0000-0002-2705-4776"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Markarian, Nikita","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5051537481"],"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.5048999786376953,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.5048999786376953,"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":0.25999999046325684,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.09099999815225601,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/drinfeld-associator","display_name":"Drinfeld associator","score":0.9990000128746033},{"id":"https://openalex.org/keywords/mixed-hodge-structures","display_name":"mixed Hodge structures","score":0.9269999861717224},{"id":"https://openalex.org/keywords/weight-filtration","display_name":"weight filtration","score":0.7269999980926514},{"id":"https://openalex.org/keywords/local-monodromy","display_name":"local monodromy","score":0.7549999952316284},{"id":"https://openalex.org/keywords/vanishing-cycles","display_name":"vanishing cycles","score":0.6320000290870667},{"id":"https://openalex.org/keywords/projective-line-minus-three-points","display_name":"projective line minus three points","score":0.7620000243186951}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8564000129699707},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6769000291824341},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.5322999954223633},{"id":"https://openalex.org/C2776933995","wikidata":"https://www.wikidata.org/wiki/Q4444341","display_name":"Hodge structure","level":3,"score":0.48730000853538513},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45969998836517334},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.4544000029563904},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.42239999771118164},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.42100000381469727},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C155069649","wikidata":"https://www.wikidata.org/wiki/Q1317202","display_name":"Hodge theory","level":3,"score":0.39239999651908875},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.34869998693466187},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.32359999418258667},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C205633959","wikidata":"https://www.wikidata.org/wiki/Q2494915","display_name":"Unipotent","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C54678060","wikidata":"https://www.wikidata.org/wiki/Q1143138","display_name":"Hodge conjecture","level":4,"score":0.27649998664855957},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C122129529","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse system","level":3,"score":0.2578999996185303},{"id":"https://openalex.org/C114417882","wikidata":"https://www.wikidata.org/wiki/Q1622692","display_name":"Hodge dual","level":4,"score":0.2574000060558319},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.19341","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19341","pdf_url":"https://arxiv.org/pdf/2609.19341","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.2609.19341","doi":"https://doi.org/10.48550/arxiv.2609.19341","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.19341","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.19341","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19341","pdf_url":"https://arxiv.org/pdf/2609.19341","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213601897.pdf","grobid_xml":"https://content.openalex.org/works/W7213601897.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7158510873"],"related_works":["https://openalex.org/W7213940488","https://openalex.org/W1967117358","https://openalex.org/W7075605200","https://openalex.org/W2963789341","https://openalex.org/W4244544029","https://openalex.org/W2921449258","https://openalex.org/W2921905706","https://openalex.org/W1497709275","https://openalex.org/W2498218857","https://openalex.org/W2089161561"],"abstract_inverted_index":{"We":[0,67,95],"compare":[1],"two":[2,48],"mixed":[3,14],"Hodge":[4,65,71,107],"structures":[5,16,49],"attached":[6],"to":[7],"a":[8,80,98],"unipotent":[9],"variation":[10],"$\\mathbb":[11],"V$":[12],"of":[13,22,83,102,105,111],"Hodge--Tate":[15],"on":[17,50],"$X=\\mathbb":[18],"P^1\\setminus{0,1,\\infty}$:":[19],"the":[20,35,69,84,103,106],"cohomology":[21],"its":[23],"extension":[24],"by":[25,30,79,89],"$*$":[26],"at":[27,32,38],"$0$":[28],"and":[29,34],"$!$":[31],"$\\infty$,":[33],"vanishing":[36],"cycles":[37],"$1$.":[39],"The":[40],"semi-holonomy":[41],"isomorphism":[42],"constructed":[43],"in":[44,109],"[arXiv:2604.26357]":[45],"identifies":[46],"these":[47],"their":[51,57,64],"underlying":[52],"rational":[53],"structures,":[54],"compatibly":[55],"with":[56,97],"weight":[58],"filtrations,":[59],"but":[60],"need":[61],"not":[62],"respect":[63],"filtrations.":[66],"compute":[68],"resulting":[70],"defect.":[72],"Its":[73],"universal":[74],"noncommutative":[75],"series":[76],"is":[77],"given":[78],"specific":[81],"component":[82],"inverse":[85],"Drinfeld":[86],"associator":[87],"multiplied":[88],"an":[90],"explicit":[91],"local":[92],"monodromy":[93],"factor.":[94],"conclude":[96],"formal":[99],"$A_\\infty$":[100],"interpretation":[101],"coefficients":[104],"defect":[108],"terms":[110],"weight-framed":[112],"Tate":[113],"extensions.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}
