{"id":"https://openalex.org/W7220664111","doi":"https://doi.org/10.48550/arxiv.2610.04234","title":"Homotopy rigidity for quasitoric manifolds over a product of simplices","display_name":"Homotopy rigidity for quasitoric manifolds over a product of simplices","publication_year":2026,"publication_date":"2026-10-03","ids":{"openalex":"https://openalex.org/W7220664111","doi":"https://doi.org/10.48550/arxiv.2610.04234"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04234","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04234","pdf_url":"https://arxiv.org/pdf/2610.04234","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/2610.04234","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157737934","display_name":"Xin Fu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4403928334","display_name":"Shanghai Institute for Mathematics and Interdisciplinary Sciences","ror":"https://ror.org/0489cd473","country_code":"CN","type":"government","lineage":["https://openalex.org/I4403928334"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fu, Xin","raw_affiliation_strings":["Shanghai Institute for Mathematics and Interdisciplinary Sciences , Shanghai 200433 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Institute for Mathematics and Interdisciplinary Sciences , Shanghai 200433 , China","institution_ids":["https://openalex.org/I4403928334"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074065226","display_name":"Tseleung So","orcid":"https://orcid.org/0000-0003-3196-6556","observed_orcids":["https://orcid.org/0000-0003-3196-6556"]},"institutions":[{"id":"https://openalex.org/I4403928334","display_name":"Shanghai Institute for Mathematics and Interdisciplinary Sciences","ror":"https://ror.org/0489cd473","country_code":"CN","type":"government","lineage":["https://openalex.org/I4403928334"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"So, Tseleung","raw_affiliation_strings":["Shanghai Institute for Mathematics and Interdisciplinary Sciences , Shanghai 200433 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Institute for Mathematics and Interdisciplinary Sciences , Shanghai 200433 , China","institution_ids":["https://openalex.org/I4403928334"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066520049","display_name":"Jongbaek Song","orcid":"https://orcid.org/0000-0002-8367-9973","observed_orcids":["https://orcid.org/0000-0002-8367-9973"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Song, Jongbaek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081484804","display_name":"Stephen Theriault","orcid":"https://orcid.org/0000-0002-7729-5527","observed_orcids":["https://orcid.org/0000-0002-7729-5527"]},"institutions":[{"id":"https://openalex.org/I4403928334","display_name":"Shanghai Institute for Mathematics and Interdisciplinary Sciences","ror":"https://ror.org/0489cd473","country_code":"CN","type":"government","lineage":["https://openalex.org/I4403928334"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Theriault, Stephen","raw_affiliation_strings":["Shanghai Institute for Mathematics and Interdisciplinary Sciences , Shanghai 200433 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Institute for Mathematics and Interdisciplinary Sciences , Shanghai 200433 , China","institution_ids":["https://openalex.org/I4403928334"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9286999702453613,"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":0.9286999702453613,"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":0.037300001829862595,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.01140000019222498,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/quasitoric-manifolds","display_name":"quasitoric manifolds","score":0.972000002861023},{"id":"https://openalex.org/keywords/cohomology-ring","display_name":"cohomology ring","score":0.8759999871253967},{"id":"https://openalex.org/keywords/polytopes","display_name":"polytopes","score":0.7250000238418579},{"id":"https://openalex.org/keywords/homotopy-equivalence","display_name":"homotopy equivalence","score":0.8550000190734863}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8242999911308289},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.8219000101089478},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.6789000034332275},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.5978000164031982},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5899999737739563},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.5394999980926514},{"id":"https://openalex.org/C35234519","wikidata":"https://www.wikidata.org/wiki/Q3983973","display_name":"Homotopy lifting property","level":4,"score":0.5236999988555908},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.5228000283241272},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.49619999527931213},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.4742000102996826},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4244999885559082},{"id":"https://openalex.org/C58193220","wikidata":"https://www.wikidata.org/wiki/Q1778193","display_name":"Direct product","level":2,"score":0.3961000144481659},{"id":"https://openalex.org/C191752858","wikidata":"https://www.wikidata.org/wiki/Q6358325","display_name":"n-connected","level":3,"score":0.39169999957084656},{"id":"https://openalex.org/C126867241","wikidata":"https://www.wikidata.org/wiki/Q3388699","display_name":"Cup product","level":5,"score":0.366100013256073},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.35179999470710754},{"id":"https://openalex.org/C168334404","wikidata":"https://www.wikidata.org/wiki/Q7309601","display_name":"Regular homotopy","level":4,"score":0.34869998693466187},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32010000944137573},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C164043645","wikidata":"https://www.wikidata.org/wiki/Q16879377","display_name":"Homotopy hypothesis","level":5,"score":0.272599995136261}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04234","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04234","pdf_url":"https://arxiv.org/pdf/2610.04234","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.2610.04234","doi":"https://doi.org/10.48550/arxiv.2610.04234","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04234","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:2610.04234","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04234","pdf_url":"https://arxiv.org/pdf/2610.04234","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/W7220664111.pdf","grobid_xml":"https://content.openalex.org/works/W7220664111.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7215033463"],"related_works":["https://openalex.org/W4396651105","https://openalex.org/W4403114570","https://openalex.org/W7096935945","https://openalex.org/W2297616800","https://openalex.org/W2131230810","https://openalex.org/W2376033291","https://openalex.org/W2963238127","https://openalex.org/W3103572594","https://openalex.org/W3103594878","https://openalex.org/W2949852420"],"abstract_inverted_index":{"We":[0,21],"consider":[1],"a":[2,41],"variation":[3],"of":[4,36,38,43,57],"the":[5,33],"Cohomological":[6],"Rigidity":[7],"Problem:":[8],"whether":[9],"two":[10,25],"quasitoric":[11,26],"manifolds":[12,27],"whose":[13],"cohomology":[14,30],"rings":[15,31],"are":[16,18,47],"isomorphic":[17,29],"homotopy":[19,48],"equivalent.":[20],"show":[22],"that":[23],"if":[24],"have":[28],"and":[32],"associated":[34],"polytope":[35],"one":[37],"them":[39],"is":[40],"product":[42],"simplices,":[44],"then":[45],"they":[46],"equivalent":[49],"after":[50],"localizing":[51],"away":[52],"from":[53],"an":[54],"explicit":[55],"list":[56],"primes.":[58]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}