{"id":"https://openalex.org/W7212065640","doi":"https://doi.org/10.48550/arxiv.2609.06345","title":"Aspherical manifolds with nonvanishing tautological classes","display_name":"Aspherical manifolds with nonvanishing tautological classes","publication_year":2026,"publication_date":"2026-09-06","ids":{"openalex":"https://openalex.org/W7212065640","doi":"https://doi.org/10.48550/arxiv.2609.06345"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.06345","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06345","pdf_url":"https://arxiv.org/pdf/2609.06345","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/2609.06345","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133216437","display_name":"Mauricio Bustamante","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I162148367","display_name":"Pontificia Universidad Cat\u00f3lica de Chile","ror":"https://ror.org/04teye511","country_code":"CL","type":"education","lineage":["https://openalex.org/I162148367"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Bustamante, Mauricio","raw_affiliation_strings":["Departamento de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile","institution_ids":["https://openalex.org/I162148367"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5133216437"],"corresponding_institution_ids":["https://openalex.org/I162148367"],"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":0.9810000061988831,"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":0.9810000061988831,"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":0.01769999973475933,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.00019999999494757503,"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/aspherical-manifolds","display_name":"aspherical manifolds","score":1.0},{"id":"https://openalex.org/keywords/tautological-classes","display_name":"tautological classes","score":0.9810000061988831},{"id":"https://openalex.org/keywords/classifying-spaces","display_name":"classifying spaces","score":0.6990000009536743},{"id":"https://openalex.org/keywords/odd-dimensional-manifolds","display_name":"odd-dimensional manifolds","score":0.8149999976158142},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.34299999475479126}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7117000222206116},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7081999778747559},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6550999879837036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6514000296592712},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6057000160217285},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5677000284194946},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5335999727249146},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4683000147342682},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C143782950","wikidata":"https://www.wikidata.org/wiki/Q40460","display_name":"Orbifold","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.37049999833106995},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30489999055862427},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2639000117778778}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.06345","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06345","pdf_url":"https://arxiv.org/pdf/2609.06345","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.2609.06345","doi":"https://doi.org/10.48550/arxiv.2609.06345","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.06345","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:2609.06345","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06345","pdf_url":"https://arxiv.org/pdf/2609.06345","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212065640.pdf","grobid_xml":"https://content.openalex.org/works/W7212065640.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2124850486","https://openalex.org/W2614666082","https://openalex.org/W1606983082","https://openalex.org/W7095326005","https://openalex.org/W4213361516","https://openalex.org/W7098015319","https://openalex.org/W2135051348","https://openalex.org/W7099901145","https://openalex.org/W7172259382","https://openalex.org/W7098644389"],"abstract_inverted_index":{"For":[0],"every":[1],"even":[2],"integer":[3],"$m\\geq":[4],"2$,":[5],"we":[6],"construct":[7],"a":[8,69],"closed,":[9],"orientable,":[10],"smooth,":[11],"aspherical":[12],"$(2m+1)$-manifold":[13],"whose":[14],"fundamental":[15],"group":[16,36],"has":[17],"nontrivial":[18],"center":[19],"and":[20,43],"for":[21],"which":[22],"infinitely":[23],"many":[24],"tautological":[25],"classes":[26],"in":[27],"the":[28,31,47],"$\\mathbb{F}_2$-cohomology":[29],"of":[30,34,37,55,71],"classifying":[32],"space":[33],"its":[35],"homotopically":[38],"trivial":[39],"diffeomorphisms":[40],"are":[41],"nonzero":[42],"not":[44,60],"nilpotent.":[45],"Specializing":[46],"calculation":[48],"to":[49,68],"cohomological":[50],"degree":[51],"$0$":[52],"gives":[53],"examples":[54],"such":[56],"manifolds":[57],"that":[58],"do":[59],"bound":[61],"compact":[62],"smooth":[63],"manifolds.":[64],"These":[65],"provide":[66],"counterexamples":[67],"conjecture":[70],"Hebestreit--Land--L\u00fcck--Randal-Williams.":[72]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-10T00:00:00"}