{"id":"https://openalex.org/W4295872273","doi":"https://doi.org/10.48550/arxiv.2209.04738","title":"Spaces of flattenings of spheres","display_name":"Spaces of flattenings of spheres","publication_year":2022,"publication_date":"2022-09-10","ids":{"openalex":"https://openalex.org/W4295872273","doi":"https://doi.org/10.48550/arxiv.2209.04738"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2209.04738","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.04738","pdf_url":"https://arxiv.org/pdf/2209.04738","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/2209.04738","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058783345","display_name":"Olakunle S. Abawonse","orcid":"https://orcid.org/0009-0004-6517-0606","observed_orcids":["https://orcid.org/0009-0004-6517-0606"]},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Abawonse, Olakunle S","raw_affiliation_strings":["Department of Mathematics , Northeastern University , 360 Huntington Ave , Boston , 02115 , Massachusetts , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Northeastern University , 360 Huntington Ave , Boston , 02115 , Massachusetts , USA","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058783345"],"corresponding_institution_ids":["https://openalex.org/I12912129"],"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":0.9262999892234802,"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":0.9262999892234802,"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":0.07000000029802322,"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":0.0005000000237487257,"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/simplicial-spheres","display_name":"simplicial spheres","score":0.9580000042915344},{"id":"https://openalex.org/keywords/differentiable-structures","display_name":"differentiable structures","score":0.7699999809265137},{"id":"https://openalex.org/keywords/homotopy-type","display_name":"homotopy type","score":0.7940000295639038},{"id":"https://openalex.org/keywords/orthogonal-group","display_name":"orthogonal group","score":0.9909999966621399}],"concepts":[{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.6695806980133057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6472072601318359},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5981968641281128},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.5509712100028992},{"id":"https://openalex.org/C64245159","wikidata":"https://www.wikidata.org/wiki/Q3983972","display_name":"Simplicial approximation theorem","level":5,"score":0.5406903624534607},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5338906645774841},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.5218945145606995},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5181280970573425},{"id":"https://openalex.org/C146867743","wikidata":"https://www.wikidata.org/wiki/Q4669959","display_name":"Abstract simplicial complex","level":3,"score":0.4574531614780426},{"id":"https://openalex.org/C97172818","wikidata":"https://www.wikidata.org/wiki/Q7520904","display_name":"Simplicial manifold","level":5,"score":0.4499666094779968},{"id":"https://openalex.org/C155366967","wikidata":"https://www.wikidata.org/wiki/Q1467124","display_name":"Simplicial set","level":4,"score":0.2996302843093872},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27484583854675293},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.16746580600738525},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11427581310272217},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2209.04738","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.04738","pdf_url":"https://arxiv.org/pdf/2209.04738","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.2209.04738","doi":"https://doi.org/10.48550/arxiv.2209.04738","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2209.04738","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2209.04738","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.04738","pdf_url":"https://arxiv.org/pdf/2209.04738","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/W4295872273.pdf","grobid_xml":"https://content.openalex.org/works/W4295872273.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2001367217","https://openalex.org/W2312859838","https://openalex.org/W2314854180","https://openalex.org/W4212938248","https://openalex.org/W4385496468"],"related_works":["https://openalex.org/W2110299047","https://openalex.org/W644098246","https://openalex.org/W2481382550","https://openalex.org/W2314216204","https://openalex.org/W4378938697","https://openalex.org/W2037592822","https://openalex.org/W2783924653","https://openalex.org/W123617326","https://openalex.org/W1986955217","https://openalex.org/W2054192452"],"abstract_inverted_index":{"The":[0],"spaces":[1,34],"of":[2,4,15,19,35,37,49],"flattenings":[3,36],"a":[5,9,23],"simplicial":[6,24,39],"sphere":[7],"played":[8],"key":[10],"role":[11],"in":[12],"the":[13,33,46,50],"study":[14],"existence":[16],"and":[17,41],"uniqueness":[18],"differentiable":[20],"structures":[21],"on":[22],"sphere.":[25],"In":[26],"this":[27],"paper,":[28],"we":[29],"will":[30],"establish":[31],"that":[32,43],"some":[38],"spheres":[40],"show":[42],"they":[44],"have":[45],"homotopy":[47],"type":[48],"orthogonal":[51],"group.":[52]},"counts_by_year":[],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2022-09-15T00:00:00"}
