{"id":"https://openalex.org/W7216516332","doi":"https://doi.org/10.48550/arxiv.2610.01776","title":"Sections, pseudosections, and multisections of Lefschetz fibrations","display_name":"Sections, pseudosections, and multisections of Lefschetz fibrations","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216516332","doi":"https://doi.org/10.48550/arxiv.2610.01776"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.01776","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01776","pdf_url":"https://arxiv.org/pdf/2610.01776","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/2610.01776","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5155046966","display_name":"R. Inanc Baykur","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Baykur, R. Inanc","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075593183","display_name":"Noriyuki Hamada","orcid":"https://orcid.org/0000-0002-1210-2800","observed_orcids":["https://orcid.org/0000-0002-1210-2800"]},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]},{"id":"https://openalex.org/I4405286446","display_name":"Institute of Mathematics for Industry, Kyushu University","ror":"https://ror.org/0257yze86","country_code":"JP","type":"facility","lineage":["https://openalex.org/I135598925","https://openalex.org/I4405286446"]}],"countries":["JP","US"],"is_corresponding":false,"raw_author_name":"Hamada, Noriyuki","raw_affiliation_strings":["Department of Mathematics and Statistics , University of Massachusetts , Amherst , MA 01003 , USA","Institute of Mathematics for Industry , Kyushu University , Fukuoka 819-0395 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , University of Massachusetts , Amherst , MA 01003 , USA","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"Institute of Mathematics for Industry , Kyushu University , Fukuoka 819-0395 , Japan","institution_ids":["https://openalex.org/I135598925","https://openalex.org/I4405286446"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lefschetz-fibrations","display_name":"Lefschetz fibrations","score":0.9710000157356262},{"id":"https://openalex.org/keywords/pseudosections","display_name":"pseudosections","score":0.8370000123977661},{"id":"https://openalex.org/keywords/multisections","display_name":"multisections","score":0.9909999966621399},{"id":"https://openalex.org/keywords/handle-decompositions","display_name":"handle decompositions","score":0.8640000224113464},{"id":"https://openalex.org/keywords/symplectic-4-manifolds","display_name":"symplectic 4-manifolds","score":0.8100000023841858}],"concepts":[{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.8948000073432922},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8884999752044678},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.8725000023841858},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.6952000260353088},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5924999713897705},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.4869999885559082},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.40459999442100525},{"id":"https://openalex.org/C172939862","wikidata":"https://www.wikidata.org/wiki/Q657469","display_name":"Lefschetz fixed-point theorem","level":5,"score":0.39890000224113464},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.313400000333786},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2732999920845032},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.2590999901294708}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.01776","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01776","pdf_url":"https://arxiv.org/pdf/2610.01776","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.2610.01776","doi":"https://doi.org/10.48550/arxiv.2610.01776","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.01776","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:2610.01776","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01776","pdf_url":"https://arxiv.org/pdf/2610.01776","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/W7216516332.pdf","grobid_xml":"https://content.openalex.org/works/W7216516332.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2541274653","https://openalex.org/W4403781148","https://openalex.org/W6966790864","https://openalex.org/W7154351877"],"related_works":["https://openalex.org/W79072886","https://openalex.org/W2228533866","https://openalex.org/W4403781148","https://openalex.org/W1883489583","https://openalex.org/W1599912090","https://openalex.org/W3094173031","https://openalex.org/W6966790864","https://openalex.org/W4300366369","https://openalex.org/W7154351877","https://openalex.org/W2594882099"],"abstract_inverted_index":{"We":[0,80],"show":[1,60],"that":[2,61],"not":[3],"every":[4,62,87],"symplectic":[5,96],"Lefschetz":[6,55,63,84,97],"fibration":[7,64],"over":[8,65],"the":[9,39,44],"$2$--sphere":[10],"admits":[11,67],"a":[12,16,25],"smooth":[13],"section,":[14],"settling":[15],"long-standing":[17],"open":[18],"problem.":[19],"To":[20],"prove":[21],"this,":[22],"we":[23,59],"develop":[24],"method":[26],"for":[27],"studying":[28],"sections":[29],"via":[30],"lifts":[31],"of":[32,43,54,71,86,99,105],"monodromy":[33],"factorizations":[34],"with":[35,77],"point-pushing":[36],"maps":[37],"and":[38,47],"induced":[40],"handle":[41],"decomposition":[42],"total":[45],"space,":[46],"apply":[48],"it":[49],"to":[50],"an":[51],"infinite":[52],"family":[53],"fibrations.":[56],"In":[57],"contrast,":[58],"$S^2$":[66],"positive":[68],"multisections.":[69],"Some":[70],"these":[72,106],"examples":[73],"admit":[74],"no":[75],"multisections":[76],"spherical":[78],"components.":[79],"also":[81],"construct":[82],"signature-zero":[83],"fibrations":[85,98],"odd":[88],"genus":[89],"$g\\geq":[90],"7$,":[91],"which":[92],"in":[93,103],"turn":[94],"give":[95],"any":[100],"prescribed":[101],"signature":[102],"each":[104],"genera.":[107]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}