{"id":"https://openalex.org/W7220675972","doi":"https://doi.org/10.48550/arxiv.2610.05480","title":"Failure of Ordinary TQFTs to Distinguish Homotopy Type","display_name":"Failure of Ordinary TQFTs to Distinguish Homotopy Type","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220675972","doi":"https://doi.org/10.48550/arxiv.2610.05480"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05480","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05480","pdf_url":"https://arxiv.org/pdf/2610.05480","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/2610.05480","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135928908","display_name":"Katherine Anne Novey","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Novey, Katherine","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5135928908"],"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.8788999915122986,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.8788999915122986,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.11590000241994858,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0005000000237487257,"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/topological-quantum-field-theory","display_name":"topological field theory","score":0.9660000205039978},{"id":"https://openalex.org/keywords/homotopy-type","display_name":"homotopy type","score":0.7910000085830688},{"id":"https://openalex.org/keywords/diffeomorphism-classification","display_name":"diffeomorphism classification","score":0.6779999732971191},{"id":"https://openalex.org/keywords/6-manifolds","display_name":"6-manifolds","score":0.7960000038146973},{"id":"https://openalex.org/keywords/simply-connected-manifolds","display_name":"simply connected manifolds","score":0.7739999890327454},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.6570000052452087}],"concepts":[{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.9006999731063843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8174999952316284},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.7940999865531921},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6136999726295471},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.6083999872207642},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5756999850273132},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.550599992275238},{"id":"https://openalex.org/C168334404","wikidata":"https://www.wikidata.org/wiki/Q7309601","display_name":"Regular homotopy","level":4,"score":0.5149999856948853},{"id":"https://openalex.org/C150275644","wikidata":"https://www.wikidata.org/wiki/Q1048949","display_name":"Cofibration","level":5,"score":0.4147999882698059},{"id":"https://openalex.org/C191752858","wikidata":"https://www.wikidata.org/wiki/Q6358325","display_name":"n-connected","level":3,"score":0.4108000099658966},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C35234519","wikidata":"https://www.wikidata.org/wiki/Q3983973","display_name":"Homotopy lifting property","level":4,"score":0.3222000002861023},{"id":"https://openalex.org/C50955798","wikidata":"https://www.wikidata.org/wiki/Q1890389","display_name":"Connected sum","level":3,"score":0.3158999979496002},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.3086000084877014},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2921000123023987},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.2646999955177307},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.26420000195503235}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05480","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05480","pdf_url":"https://arxiv.org/pdf/2610.05480","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.2610.05480","doi":"https://doi.org/10.48550/arxiv.2610.05480","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05480","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:2610.05480","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05480","pdf_url":"https://arxiv.org/pdf/2610.05480","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/W7220675972.pdf","grobid_xml":"https://content.openalex.org/works/W7220675972.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W2170604368","https://openalex.org/W2980982072","https://openalex.org/W3196315773","https://openalex.org/W4280502437","https://openalex.org/W4286979695","https://openalex.org/W4402953197","https://openalex.org/W4405721356","https://openalex.org/W4415355229","https://openalex.org/W7126112259"],"related_works":["https://openalex.org/W7126112259","https://openalex.org/W3087582932","https://openalex.org/W143834982","https://openalex.org/W4364361459","https://openalex.org/W7134989411","https://openalex.org/W7169855423","https://openalex.org/W3196315773","https://openalex.org/W4415037433","https://openalex.org/W2160953844","https://openalex.org/W2941514417"],"abstract_inverted_index":{"Work":[0],"by":[1,48,119,176,218],"David":[2],"Reutter":[3],"and":[4,41,75,154,169,198],"Christopher":[5],"Schommer-Pries":[6],"has":[7],"shown":[8],"that":[9,111,132,161,209],"ordinary":[10,49,120,133,219],"smooth":[11,33,76,95],"TQFTs":[12,70,121,134],"can":[13],"distinguish":[14,136],"(stable)":[15],"diffeomorphism":[16],"classes":[17],"of":[18,53,72,83,103,140,164,174,189,205],"closed,":[19,32],"connected,":[20,31],"even-dimensional":[21],"manifolds":[22,144],"subject":[23],"to":[24,130,152,192],"certain":[25],"finiteness":[26],"conditions.":[27],"In":[28],"particular,":[29],"simply":[30,62,104,141],"6-manifolds":[34,65,107],"with":[35,108],"finite":[36],"$\u03c0_2$":[37,110],"are":[38,112,117,210],"diffeomorphic":[39],"if":[40,43],"only":[42],"they":[44],"cannot":[45,135,215],"be":[46,216],"distinguished":[47,217],"TQFTs.":[50,220],"The":[51],"question":[52],"whether":[54],"or":[55,150],"not":[56,113,211],"this":[57,90,128],"result":[58],"holds":[59],"for":[60,195],"all":[61,123,146,196],"connected":[63,105,142,156,180,187],"closed":[64,106,143,157,207],"was":[66],"open.":[67],"We":[68,99,126,159],"consider":[69],"out":[71,82],"the":[73,93,137],"topological":[74],"bordism":[77,86,97],"categories,":[78],"as":[79,81],"well":[80],"a":[84,101,171,178,203],"new":[85],"category":[87],"constructed":[88],"in":[89,122,145],"paper":[91],"called":[92],"formally":[94],"(FS)":[96],"category.":[98],"present":[100,170],"pair":[102,204],"infinite":[109],"homotopy":[114,138,212],"equivalent,":[115,213],"yet":[116,214],"indistinguishable":[118],"three":[124],"categories.":[125],"extend":[127],"counter-example":[129,165],"show":[131,160,193],"type":[139],"dimensions":[147],"greater":[148],"than":[149],"equal":[151],"6":[153],"non-simply":[155],"5-manifolds.":[158],"our":[162,190],"class":[163,173],"pairs":[166],"is":[167,202],"spinnable":[168],"non-spinnable":[172],"counter-examples":[175,191],"introducing":[177],"$\\mathbb{C}P^2$":[179],"summand.":[181],"Lastly,":[182],"we":[183],"use":[184],"more":[185],"highly":[186],"analogues":[188],"that,":[194],"$n\\geq2$":[197],"$m\\geq":[199],"2n$,":[200],"there":[201],"$(2n-1)$-connected":[206],"$(4n+m)$-manifolds":[208]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
