{"id":"https://openalex.org/W7204481371","doi":"https://doi.org/10.48550/arxiv.2608.25725","title":"Gr\u00f6bner Bases for Alexander Fitting Ideals of Links","display_name":"Gr\u00f6bner Bases for Alexander Fitting Ideals of Links","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7204481371","doi":"https://doi.org/10.48550/arxiv.2608.25725"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.25725","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.25725","pdf_url":"https://arxiv.org/pdf/2608.25725","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","license_id":"https://openalex.org/licenses/cc-by","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/2608.25725","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057871998","display_name":"Takefumi Nosaka","orcid":"https://orcid.org/0000-0001-7901-8673","observed_orcids":["https://orcid.org/0000-0001-7901-8673"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nosaka, Takefumi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5148415992","display_name":"Kotaro Shimizu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shimizu, Kotaro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.9848999977111816,"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":0.9848999977111816,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.002099999925121665,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/grobner-bases","display_name":"Gr\u00f6bner bases","score":0.8330000042915344},{"id":"https://openalex.org/keywords/links","display_name":"links","score":0.7210000157356262},{"id":"https://openalex.org/keywords/torus-links","display_name":"torus links","score":0.8090000152587891},{"id":"https://openalex.org/keywords/pretzel-links","display_name":"pretzel links","score":0.9679999947547913},{"id":"https://openalex.org/keywords/3-manifolds","display_name":"3-manifolds","score":0.8759999871253967}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8205000162124634},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.6960999965667725},{"id":"https://openalex.org/C169903001","wikidata":"https://www.wikidata.org/wiki/Q3264987","display_name":"Reciprocity (cultural anthropology)","level":2,"score":0.6468999981880188},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5924000144004822},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5444999933242798},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.48890000581741333},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4399000108242035},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4327000081539154},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4205999970436096},{"id":"https://openalex.org/C129946241","wikidata":"https://www.wikidata.org/wiki/Q1634206","display_name":"Alexander polynomial","level":4,"score":0.4198000133037567},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3937000036239624},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.3919999897480011},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3749000132083893},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.2614000141620636},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.25725","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.25725","pdf_url":"https://arxiv.org/pdf/2608.25725","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.25725","doi":"https://doi.org/10.48550/arxiv.2608.25725","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.25725","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.25725","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.25725","pdf_url":"https://arxiv.org/pdf/2608.25725","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","license_id":"https://openalex.org/licenses/cc-by","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/W7204481371.pdf","grobid_xml":"https://content.openalex.org/works/W7204481371.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2071368642","https://openalex.org/W2942310033"],"related_works":["https://openalex.org/W1575757266","https://openalex.org/W7099984630","https://openalex.org/W1503953695","https://openalex.org/W2034512420","https://openalex.org/W4404721966","https://openalex.org/W75038760","https://openalex.org/W2229872410","https://openalex.org/W3197243948","https://openalex.org/W2080315469","https://openalex.org/W2242374482"],"abstract_inverted_index":{"Multivariable":[0],"Alexander":[1],"theory":[2],"produces":[3],"Fitting":[4],"ideals":[5,21],"without":[6],"preferred":[7],"generators.":[8],"After":[9],"fixing":[10],"a":[11,15,45,54,81],"coefficient":[12,42],"field":[13],"and":[14,73,76],"monomial":[16],"order,":[17],"we":[18,59,77],"represent":[19],"these":[20,68],"by":[22],"reduced":[23],"Gr\u00f6bner":[24],"bases":[25],"of":[26,33,44,57],"their":[27],"polynomial":[28],"contractions,":[29],"obtaining":[30],"Alexander--Gr\u00f6bner":[31],"invariants":[32,69],"links.":[34],"Over":[35],"\\(\\mathbb":[36],"Q\\),":[37],"for":[38,70,80],"the":[39],"maximal":[40],"free-abelian":[41],"system":[43],"connected":[46],"compact":[47],"oriented":[48],"\\(3\\)-manifold":[49],"whose":[50],"nonempty":[51],"boundary":[52],"is":[53],"disjoint":[55],"union":[56],"tori,":[58],"deduce":[60],"determinant-divisor":[61],"reciprocity":[62],"from":[63],"Blanchfield":[64],"duality.":[65],"We":[66],"compute":[67],"torus":[71],"links":[72],"low-crossing":[74],"links,":[75],"determine":[78],"\\(\\AG_2\\)":[79],"two-component":[82],"pretzel":[83],"family.":[84]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-28T00:00:00"}
