{"id":"https://openalex.org/W7140212876","doi":"https://doi.org/10.48550/arxiv.2603.21431","title":"Cocycles and positive functionals in higher cohomology","display_name":"Cocycles and positive functionals in higher cohomology","publication_year":2026,"publication_date":"2026-03-22","ids":{"openalex":"https://openalex.org/W7140212876","doi":"https://doi.org/10.48550/arxiv.2603.21431"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2603.21431","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.21431","pdf_url":"https://arxiv.org/pdf/2603.21431","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2603.21431","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046503637","display_name":"Antonio L\u00f3pez Neumann","orcid":"https://orcid.org/0009-0001-6372-8811","observed_orcids":["https://orcid.org/0009-0001-6372-8811"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Neumann, Antonio L\u00f3pez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011979341","display_name":"Piotr W. Nowak","orcid":"https://orcid.org/0000-0002-6519-004X","observed_orcids":["https://orcid.org/0000-0002-6519-004X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nowak, Piotr W.","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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9984999895095825,"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":0.9984999895095825,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0003000000142492354,"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/T10884","display_name":"Holomorphic and Operator Theory","score":9.999999747378752e-05,"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/positive-functionals","display_name":"positive functionals","score":0.8169999718666077},{"id":"https://openalex.org/keywords/cocycles","display_name":"cocycles","score":0.8830000162124634},{"id":"https://openalex.org/keywords/gns-construction","display_name":"GNS construction","score":0.8980000019073486},{"id":"https://openalex.org/keywords/extension-property","display_name":"extension property","score":0.6499999761581421},{"id":"https://openalex.org/keywords/vanishing-of-cohomology","display_name":"cohomology vanishing","score":0.8240000009536743},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.753000020980835},{"id":"https://openalex.org/keywords/reduced-cohomology","display_name":"reduced cohomology","score":0.6510000228881836}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8529000282287598},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7322999835014343},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.7222999930381775},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.6974999904632568},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5386999845504761},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5266000032424927},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5133000016212463},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C178609977","wikidata":"https://www.wikidata.org/wiki/Q3503315","display_name":"Spectral sequence","level":3,"score":0.329800009727478},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C155751095","wikidata":"https://www.wikidata.org/wiki/Q1408937","display_name":"Group cohomology","level":3,"score":0.28279998898506165},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C74196217","wikidata":"https://www.wikidata.org/wiki/Q1095535","display_name":"\u010cech cohomology","level":5,"score":0.2689000070095062},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2581999897956848},{"id":"https://openalex.org/C145054310","wikidata":"https://www.wikidata.org/wiki/Q212803","display_name":"Algebraic topology","level":3,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2603.21431","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.21431","pdf_url":"https://arxiv.org/pdf/2603.21431","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.2603.21431","doi":"https://doi.org/10.48550/arxiv.2603.21431","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.21431","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2603.21431","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.21431","pdf_url":"https://arxiv.org/pdf/2603.21431","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":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.427552193403244}],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320328290","display_name":"Fondation Sciences Math\u00e9matiques de Paris","ror":"https://ror.org/02zgjrf98"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7140212876.pdf","grobid_xml":"https://content.openalex.org/works/W7140212876.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,15,45],"establish":[1],"and":[2,9,28],"explore":[3],"the":[4,17,22,52,57],"correspondence":[5],"between":[6],"positive":[7,43],"functionals":[8],"cocycles":[10],"in":[11],"higher":[12,26,35],"unitary":[13,36,68],"cohomology.":[14],"generalize":[16],"classical":[18],"cocycle":[19],"version":[20],"of":[21,34,65,67],"Gelfand-Naimark-Segal":[23],"construction":[24],"to":[25,31],"degrees":[27],"apply":[29],"it":[30],"characterize":[32],"vanishing":[33,63],"cohomology":[37,69],"as":[38],"an":[39],"extension":[40],"property":[41],"for":[42,56],"functionals.":[44],"also":[46],"prove":[47],"that":[48],"under":[49],"mild":[50],"conditions":[51],"algebraic":[53],"spectral":[54],"gap":[55],"one":[58],"sided":[59],"Laplacian":[60],"characterizes":[61],"cohomological":[62],"instead":[64],"reducedness":[66]},"counts_by_year":[],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2026-03-25T00:00:00"}
