{"id":"https://openalex.org/W7214716160","doi":"https://doi.org/10.48550/arxiv.2609.33329","title":"Morse-Bott inequalities on Lefschetz complexes","display_name":"Morse-Bott inequalities on Lefschetz complexes","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214716160","doi":"https://doi.org/10.48550/arxiv.2609.33329"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33329","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33329","pdf_url":"https://arxiv.org/pdf/2609.33329","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/2609.33329","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120648616","display_name":"Yuto Nishikawa","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I72253084","display_name":"Saitama University","ror":"https://ror.org/02evnh647","country_code":"JP","type":"education","lineage":["https://openalex.org/I72253084"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Nishikawa, Yuto","raw_affiliation_strings":["Graduate School of Science and Engineering , Saitama University , 255 Shimo-Okubo , Sakura-ku , Saitama-shi , Saitama 338-8570 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Science and Engineering , Saitama University , 255 Shimo-Okubo , Sakura-ku , Saitama-shi , Saitama 338-8570 , Japan","institution_ids":["https://openalex.org/I72253084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5120648616"],"corresponding_institution_ids":["https://openalex.org/I72253084"],"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.5019999742507935,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.5019999742507935,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.25270000100135803,"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":0.1339000016450882,"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/morse-bott-theory","display_name":"Morse-Bott theory","score":0.8799999952316284},{"id":"https://openalex.org/keywords/discrete-morse-theory","display_name":"discrete Morse theory","score":0.7570000290870667},{"id":"https://openalex.org/keywords/poincare-series","display_name":"Poincar\u00e9 series","score":0.843999981880188},{"id":"https://openalex.org/keywords/betti-numbers","display_name":"Betti numbers","score":0.9549999833106995},{"id":"https://openalex.org/keywords/cw-complexes","display_name":"CW complexes","score":0.7329999804496765}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8889999985694885},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.8389999866485596},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7612000107765198},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5015000104904175},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.46129998564720154},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45809999108314514},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4345000088214874},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.43160000443458557},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4162999987602234},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3903000056743622},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.382099986076355},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3758000135421753},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.3594000041484833},{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C2779851814","wikidata":"https://www.wikidata.org/wiki/Q5358916","display_name":"Elementary theory","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33329","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33329","pdf_url":"https://arxiv.org/pdf/2609.33329","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.2609.33329","doi":"https://doi.org/10.48550/arxiv.2609.33329","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33329","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:2609.33329","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33329","pdf_url":"https://arxiv.org/pdf/2609.33329","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214716160.pdf","grobid_xml":"https://content.openalex.org/works/W7214716160.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W643853242","https://openalex.org/W3144527280","https://openalex.org/W4389072741","https://openalex.org/W4416189869"],"related_works":["https://openalex.org/W3144527280","https://openalex.org/W7153449472","https://openalex.org/W4416189869","https://openalex.org/W1997857162","https://openalex.org/W4387165255","https://openalex.org/W3044300456","https://openalex.org/W4205797221","https://openalex.org/W2963251750","https://openalex.org/W2045097502","https://openalex.org/W4236939312"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,24,61],"discrete":[3],"Morse-Bott":[4,43,121],"theory":[5],"for":[6,34,123],"Lefschetz":[7,124],"complexes":[8],"with":[9,41,68,145],"real-valued":[10],"incidence":[11],"functions":[12],"and":[13,49,119],"finitely":[14,55],"many":[15,56],"cells":[16,103],"in":[17,58,84,129,151],"each":[18,59,141],"dimension.":[19,154],"Our":[20],"main":[21],"result":[22],"is":[23,137],"reduction":[25],"procedure,":[26],"based":[27],"on":[28],"four":[29],"elementary":[30,66,149],"operations":[31],"called":[32],"Moves,":[33],"computing":[35],"the":[36,42,50,76,82,85,93,97,102,112,115,120,135,146,152],"remainder":[37],"series":[38],"$R_t$":[39,79,118,144],"associated":[40],"inequality.":[44],"These":[45],"Moves":[46,57],"preserve":[47],"$R_t$,":[48],"procedure":[51,90],"recursively":[52],"constructs,":[53],"using":[54],"dimension,":[60],"disjoint":[62],"union":[63],"of":[64,78,96,114,117,143,148],"two-cell":[65],"blocks":[67,83,150],"vanishing":[69],"Poincar\u00e9":[70],"series.":[71],"The":[72,88,126],"resulting":[73],"decomposition":[74],"computes":[75,92],"coefficients":[77,116],"by":[80,100,139],"counting":[81,101],"corresponding":[86,153],"dimensions.":[87],"same":[89],"also":[91],"Betti":[94],"numbers":[95],"original":[98],"complex":[99],"removed":[104],"as":[105],"isolated":[106],"cells.":[107],"As":[108],"consequences,":[109],"we":[110],"obtain":[111],"nonnegativity":[113,136],"inequality":[122],"complexes.":[125],"method":[127],"applies":[128],"particular":[130],"to":[131],"CW":[132],"complexes,":[133],"where":[134],"obtained":[138],"identifying":[140],"coefficient":[142],"number":[147]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
