{"id":"https://openalex.org/W7214285127","doi":"https://doi.org/10.48550/arxiv.2609.29561","title":"On Auroux's Luttinger-surgery uniqueness question","display_name":"On Auroux's Luttinger-surgery uniqueness question","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7214285127","doi":"https://doi.org/10.48550/arxiv.2609.29561"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29561","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29561","pdf_url":"https://arxiv.org/pdf/2609.29561","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/2609.29561","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152821430","display_name":"Nobuo Iida","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I166644833","display_name":"Kavli Institute for the Physics and Mathematics of the Universe","ror":"https://ror.org/02chw6z69","country_code":"JP","type":"facility","lineage":["https://openalex.org/I166644833","https://openalex.org/I4405286593","https://openalex.org/I74801974"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Iida, Nobuo","raw_affiliation_strings":["Kavli Institute for the Physics and Mathematics of the Universe (WPI) , The University of Tokyo , 5-1-5 Kashiwanoha , Kashiwa , Chiba 277-8583 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kavli Institute for the Physics and Mathematics of the Universe (WPI) , The University of Tokyo , 5-1-5 Kashiwanoha , Kashiwa , Chiba 277-8583 , Japan","institution_ids":["https://openalex.org/I166644833","https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5152821430"],"corresponding_institution_ids":["https://openalex.org/I166644833","https://openalex.org/I74801974"],"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":0.9907000064849854,"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":0.9907000064849854,"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":0.0032999999821186066,"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/T12351","display_name":"Geometry and complex manifolds","score":0.0024999999441206455,"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/symplectic-four-manifolds","display_name":"symplectic four-manifolds","score":0.9150000214576721},{"id":"https://openalex.org/keywords/simply-connected-manifolds","display_name":"simply connected manifolds","score":0.8220000267028809},{"id":"https://openalex.org/keywords/second-chern-class","display_name":"second Chern class","score":0.4869999885559082}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.9000999927520752},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7340999841690063},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6723999977111816},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5921000242233276},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5863000154495239},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5324000120162964},{"id":"https://openalex.org/C104586451","wikidata":"https://www.wikidata.org/wiki/Q771008","display_name":"Symplectic representation","level":4,"score":0.4878000020980835},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.4767000079154968},{"id":"https://openalex.org/C40265840","wikidata":"https://www.wikidata.org/wiki/Q6897118","display_name":"Moment map","level":3,"score":0.4731999933719635},{"id":"https://openalex.org/C125849494","wikidata":"https://www.wikidata.org/wiki/Q766774","display_name":"Symplectic vector space","level":5,"score":0.46050000190734863},{"id":"https://openalex.org/C2777969054","wikidata":"https://www.wikidata.org/wiki/Q6425087","display_name":"Kodaira dimension","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.42260000109672546},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.41609999537467957},{"id":"https://openalex.org/C207789664","wikidata":"https://www.wikidata.org/wiki/Q1547297","display_name":"Gromov\u2013Witten invariant","level":5,"score":0.31119999289512634},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C175322374","wikidata":"https://www.wikidata.org/wiki/Q936434","display_name":"Symplectic group","level":3,"score":0.28780001401901245},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.274399995803833}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29561","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29561","pdf_url":"https://arxiv.org/pdf/2609.29561","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.2609.29561","doi":"https://doi.org/10.48550/arxiv.2609.29561","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29561","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:2609.29561","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29561","pdf_url":"https://arxiv.org/pdf/2609.29561","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/F4320322832","display_name":"University of Tokyo","ror":"https://ror.org/057zh3y96"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214285127.pdf","grobid_xml":"https://content.openalex.org/works/W7214285127.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2964038182","https://openalex.org/W2021713915","https://openalex.org/W1767154005","https://openalex.org/W1597287561","https://openalex.org/W3102510610","https://openalex.org/W7098864625","https://openalex.org/W1932759423","https://openalex.org/W3101021661","https://openalex.org/W7100059442","https://openalex.org/W1527365816"],"abstract_inverted_index":{"We":[0],"construct":[1],"simply":[2],"connected":[3],"integral":[4],"symplectic":[5,22,29],"four-manifolds":[6],"forming":[7],"an":[8],"exotic":[9],"pair,":[10],"with":[11,21],"equal":[12],"values":[13],"of":[14],"$c_1^2$,":[15],"$c_2$,":[16],"$c_1\\mathbin{\\cdot}[\u03c9]$,":[17],"and":[18,26],"$[\u03c9]^2$,":[19],"but":[20],"Kodaira":[23,30],"dimensions":[24],"$-\\infty$":[25],"$2$.":[27],"Since":[28],"dimension":[31],"is":[32],"invariant":[33],"under":[34],"Luttinger":[35],"surgery,":[36],"the":[37],"two":[38],"manifolds":[39],"are":[40],"not":[41],"Luttinger-surgery":[42],"equivalent.":[43],"This":[44],"gives":[45],"a":[46],"negative":[47],"answer":[48],"to":[49],"Auroux's":[50],"uniqueness":[51],"question.":[52]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-26T00:00:00"}
