{"id":"https://openalex.org/W7223780944","doi":"https://doi.org/10.48550/arxiv.2610.33875","title":"Global invertibility of polynomial mappings and connectedness of preimages of large spheres","display_name":"Global invertibility of polynomial mappings and connectedness of preimages of large spheres","publication_year":2026,"publication_date":"2026-10-24","ids":{"openalex":"https://openalex.org/W7223780944","doi":"https://doi.org/10.48550/arxiv.2610.33875"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.33875","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33875","pdf_url":"https://arxiv.org/pdf/2610.33875","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/2610.33875","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053792587","display_name":"Francisco Braun","orcid":"https://orcid.org/0000-0003-3594-9809","observed_orcids":["https://orcid.org/0000-0003-3594-9809"]},"institutions":[{"id":"https://openalex.org/I177909021","display_name":"Universidade Federal de S\u00e3o Carlos","ror":"https://ror.org/00qdc6m37","country_code":"BR","type":"education","lineage":["https://openalex.org/I177909021"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Braun, Francisco","raw_affiliation_strings":["Departamento de Matem\u00e1tica , Universidade Federal de S\u00e3o Carlos , 13565-905 S\u00e3o Carlos , S\u00e3o Paulo , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica , Universidade Federal de S\u00e3o Carlos , 13565-905 S\u00e3o Carlos , S\u00e3o Paulo , Brazil","institution_ids":["https://openalex.org/I177909021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055079960","display_name":"Zbigniew Jelonek","orcid":"https://orcid.org/0000-0002-1065-8688","observed_orcids":["https://orcid.org/0000-0002-1065-8688"]},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jelonek, Zbigniew","raw_affiliation_strings":["Instituto de Ci\u00eancias Matem\u00e1ticas e Computac \u00b8\u00e3o , Universidade de S\u00e3o Paulo , 13566- 590 S\u00e3o Carlos , S\u00e3o Paulo , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Ci\u00eancias Matem\u00e1ticas e Computac \u00b8\u00e3o , Universidade de S\u00e3o Paulo , 13566- 590 S\u00e3o Carlos , S\u00e3o Paulo , Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009190356","display_name":"Maria Michalska","orcid":"https://orcid.org/0000-0003-4344-3832","observed_orcids":["https://orcid.org/0000-0003-4344-3832"]},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Michalska, Maria","raw_affiliation_strings":["Instytut Matematyczny , Polska Akademia Nauk , \u015aniadeckich 8 8 , 00-656 Warszawa , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instytut Matematyczny , Polska Akademia Nauk , \u015aniadeckich 8 8 , 00-656 Warszawa , Poland","institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.3474000096321106,"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":0.3474000096321106,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.27250000834465027,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.19169999659061432,"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/global-invertibility","display_name":"global invertibility","score":0.7689999938011169},{"id":"https://openalex.org/keywords/polynomial-maps","display_name":"polynomial maps","score":0.9789999723434448},{"id":"https://openalex.org/keywords/large-spheres","display_name":"large spheres","score":0.7490000128746033},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.7979999780654907}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7983999848365784},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.6686999797821045},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6474000215530396},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.6146000027656555},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5999000072479248},{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.5365999937057495},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44940000772476196},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42410001158714294},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.41119998693466187},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.36500000953674316},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34049999713897705},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2732999920845032},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.33875","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33875","pdf_url":"https://arxiv.org/pdf/2610.33875","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.2610.33875","doi":"https://doi.org/10.48550/arxiv.2610.33875","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.33875","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.33875","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33875","pdf_url":"https://arxiv.org/pdf/2610.33875","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/W7223780944.pdf","grobid_xml":"https://content.openalex.org/works/W7223780944.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3050035967","https://openalex.org/W2269724164","https://openalex.org/W19071580","https://openalex.org/W2027415339","https://openalex.org/W4393340535","https://openalex.org/W2946393951","https://openalex.org/W2126712331","https://openalex.org/W1513080731","https://openalex.org/W1980801980","https://openalex.org/W2624381663"],"abstract_inverted_index":{"We":[0],"prove":[1,51],"that":[2,52],"a":[3,15,72,77],"polynomial":[4],"mapping":[5,67],"$\\mathbb{R}^2":[6],"\\to":[7],"\\mathbb{R}^2$":[8],"with":[9,42],"nowhere":[10],"zero":[11],"Jacobian":[12],"determinant":[13],"is":[14,68],"global":[16],"diffeomorphism":[17],"provided":[18],"the":[19,54,62,66],"preimage":[20],"of":[21,36,44,56,65],"large":[22,57],"circles":[23],"are":[24,59],"connected.":[25],"In":[26],"higher":[27],"dimensions":[28],"this":[29],"result":[30],"fails":[31],"and":[32],"we":[33,50],"present":[34],"families":[35],"counterexamples.":[37],"Yet,":[38],"in":[39],"dimension":[40],"$3$":[41],"codimension":[43],"Jelonek":[45,63],"set":[46,64],"greater":[47],"than":[48],"one,":[49],"if":[53],"preimages":[55],"spheres":[58],"connected,":[60],"then":[61],"neither":[69],"homeomorphic":[70],"to":[71],"line":[73],"nor":[74],"can":[75],"have":[76],"single":[78],"end":[79],"at":[80],"infinity.":[81]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-28T00:00:00"}