{"id":"https://openalex.org/W7211894642","doi":"https://doi.org/10.48550/arxiv.2609.04440","title":"A topological version of the Cartan-Hadamard Theorem and asphericity complexity","display_name":"A topological version of the Cartan-Hadamard Theorem and asphericity complexity","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7211894642","doi":"https://doi.org/10.48550/arxiv.2609.04440"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04440","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04440","pdf_url":"https://arxiv.org/pdf/2609.04440","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/2609.04440","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051978199","display_name":"El\u00edas Gabriel Minian","orcid":"https://orcid.org/0009-0009-2879-0466","observed_orcids":["https://orcid.org/0009-0009-2879-0466"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Minian, Elias Gabriel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5150695712","display_name":"Juan Mart\u00edn Perez Garber","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Garber, Juan Mart\u00edn Perez","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/T10304","display_name":"Geometric and Algebraic Topology","score":0.8539999723434448,"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":0.8539999723434448,"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":0.09160000085830688,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.017999999225139618,"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/asphericity","display_name":"asphericity","score":0.9419999718666077},{"id":"https://openalex.org/keywords/path-space","display_name":"path space","score":0.781000018119812},{"id":"https://openalex.org/keywords/universal-cover","display_name":"universal cover","score":0.8069999814033508},{"id":"https://openalex.org/keywords/contractibility","display_name":"contractibility","score":0.652999997138977},{"id":"https://openalex.org/keywords/cw-complexes","display_name":"CW complexes","score":0.796999990940094},{"id":"https://openalex.org/keywords/fiber-bundles","display_name":"fiber bundles","score":0.5120000243186951},{"id":"https://openalex.org/keywords/continuous-sections","display_name":"continuous sections","score":0.6869999766349792}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8057000041007996},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.6754999756813049},{"id":"https://openalex.org/C169611556","wikidata":"https://www.wikidata.org/wiki/Q230689","display_name":"Contractible space","level":2,"score":0.6450999975204468},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.508899986743927},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.43860000371932983},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41929998993873596},{"id":"https://openalex.org/C2778478883","wikidata":"https://www.wikidata.org/wiki/Q7825025","display_name":"Topological complexity","level":2,"score":0.4138999879360199},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.4041000008583069},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.38940000534057617},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.38519999384880066},{"id":"https://openalex.org/C35234519","wikidata":"https://www.wikidata.org/wiki/Q3983973","display_name":"Homotopy lifting property","level":4,"score":0.3840000033378601},{"id":"https://openalex.org/C146710177","wikidata":"https://www.wikidata.org/wiki/Q1154996","display_name":"Fiber bundle","level":3,"score":0.3813999891281128},{"id":"https://openalex.org/C154804608","wikidata":"https://www.wikidata.org/wiki/Q2721559","display_name":"Topological manifold","level":5,"score":0.3659999966621399},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.3589000105857849},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.3488999903202057},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C24977911","wikidata":"https://www.wikidata.org/wiki/Q1491995","display_name":"Connected space","level":3,"score":0.2953000068664551},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C40753290","wikidata":"https://www.wikidata.org/wiki/Q1139111","display_name":"Quotient space (topology)","level":3,"score":0.28349998593330383},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28299999237060547},{"id":"https://openalex.org/C140936041","wikidata":"https://www.wikidata.org/wiki/Q1801244","display_name":"Zero-dimensional space","level":4,"score":0.2825999855995178},{"id":"https://openalex.org/C47600822","wikidata":"https://www.wikidata.org/wiki/Q7825032","display_name":"Topological dynamics","level":5,"score":0.27239999175071716},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.2689000070095062},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C59831887","wikidata":"https://www.wikidata.org/wiki/Q7887158","display_name":"Unit tangent bundle","level":4,"score":0.25940001010894775},{"id":"https://openalex.org/C162362422","wikidata":"https://www.wikidata.org/wiki/Q1363919","display_name":"Second-countable space","level":3,"score":0.25679999589920044},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.25609999895095825}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.04440","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04440","pdf_url":"https://arxiv.org/pdf/2609.04440","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.2609.04440","doi":"https://doi.org/10.48550/arxiv.2609.04440","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.04440","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:2609.04440","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04440","pdf_url":"https://arxiv.org/pdf/2609.04440","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":[{"id":"https://openalex.org/F4320335478","display_name":"Secretar\u00eda de Ciencia y T\u00e9cnica, Universidad de Buenos Aires","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7211894642.pdf","grobid_xml":"https://content.openalex.org/works/W7211894642.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4319323466"],"related_works":["https://openalex.org/W3122850890","https://openalex.org/W2944659964","https://openalex.org/W2951486115","https://openalex.org/W4404209502","https://openalex.org/W4402270496","https://openalex.org/W1915136435","https://openalex.org/W1779689530","https://openalex.org/W7057158367","https://openalex.org/W1985844501","https://openalex.org/W4407359567"],"abstract_inverted_index":{"We":[0,81,136,168],"investigate":[1],"a":[2,34,55,69,105],"topological":[3,23,197],"version":[4],"of":[5,15,20,41,44,116,122,125,158,162,165,175,178,182,195],"the":[6,26,38,49,59,73,78,87,113,120,133,149,163,173,193],"Cartan-Hadamard":[7],"theorem":[8],"that":[9,53,83,138,142],"allows":[10,153],"one":[11],"to":[12,48,58,132,155,187,192],"study":[13,172],"asphericity":[14,157,176],"spaces":[16,66,179],"via":[17],"distinguished":[18,27,74],"families":[19],"paths.":[21],"A":[22],"space":[24,39,51,102],"has":[25,86,148],"path":[28,50],"property":[29],"(dpp)":[30],"if":[31,84],"there":[32],"exists":[33],"continuous":[35,166],"map":[36],"from":[37,185],"$\u03a0(X)$":[40,103,186],"homotopy":[42],"classes":[43],"paths":[45,75],"(relative":[46],"endpoints)":[47],"$X^I$":[52,188],"is":[54,93,99,104,112,129,143],"right":[56],"inverse":[57],"canonical":[60],"quotient":[61],"map.":[62],"For":[63],"complete":[64],"metric":[65],"endowed":[67],"with":[68],"locally":[70,144],"convex":[71],"metric,":[72],"are":[76],"precisely":[77],"local":[79,183],"geodesics.":[80],"show":[82],"$X$":[85,98,109],"dpp,":[88,150],"then":[89],"its":[90],"universal":[91,114],"cover":[92,115],"contractible":[94],"and,":[95],"in":[96,119,160],"particular,":[97],"aspherical.":[100],"The":[101],"fiber":[106,111],"bundle":[107],"over":[108],"whose":[110],"$X$,":[117],"and":[118,151,171,189,202],"case":[121],"Riemannian":[123],"manifolds":[124],"non-positive":[126],"curvature":[127],"it":[128,191],"naturally":[130],"isomorphic":[131],"tangent":[134],"bundle.":[135],"prove":[137],"every":[139],"aspherical":[140],"CW-complex":[141],"finite":[145],"or":[146],"countable":[147],"this":[152],"us":[154],"reinterpret":[156],"CW-complexes":[159],"terms":[161],"existence":[164],"sections.":[167],"also":[169],"define":[170],"notion":[174],"complexity":[177,198],"by":[180,200],"means":[181],"sections":[184],"relate":[190],"concept":[194],"equivariant":[196],"introduced":[199],"Colman":[201],"Grant.":[203]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-08T00:00:00"}
