{"id":"https://openalex.org/W2559432683","doi":"https://doi.org/10.1007/s00454-021-00287-3","title":"Linking Numbers in Three-Manifolds","display_name":"Linking Numbers in Three-Manifolds","publication_year":2021,"publication_date":"2021-07-06","ids":{"openalex":"https://openalex.org/W2559432683","doi":"https://doi.org/10.1007/s00454-021-00287-3","mag":"2559432683","pmid":"https://pubmed.ncbi.nlm.nih.gov/34720305"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-021-00287-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-021-00287-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-021-00287-3.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-021-00287-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066368701","display_name":"Patricia Cahn","orcid":"https://orcid.org/0000-0002-2834-0897"},"institutions":[{"id":"https://openalex.org/I202524275","display_name":"Smith College","ror":"https://ror.org/0497crr92","country_code":"US","type":"education","lineage":["https://openalex.org/I202524275"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patricia Cahn","raw_affiliation_strings":["Smith College, Northampton, USA"],"affiliations":[{"raw_affiliation_string":"Smith College, Northampton, USA","institution_ids":["https://openalex.org/I202524275"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012600734","display_name":"Alexandra Kjuchukova","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alexandra Kjuchukova","raw_affiliation_strings":["Max Planck Institute for Mathematics, Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics, Bonn, Germany","institution_ids":["https://openalex.org/I4210119712"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012600734"],"corresponding_institution_ids":["https://openalex.org/I4210119712"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.4219,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.52573697,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"66","issue":"2","first_page":"435","last_page":"463"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998999834060669,"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":0.9998999834060669,"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/T11274","display_name":"Botulinum Toxin and Related Neurological Disorders","score":0.9444000124931335,"subfield":{"id":"https://openalex.org/subfields/2728","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.916100025177002,"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/knot","display_name":"Knot (papermaking)","score":0.6939274668693542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6587895154953003},{"id":"https://openalex.org/keywords/ribbon","display_name":"Ribbon","score":0.6520676612854004},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6336148381233215},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5440492033958435},{"id":"https://openalex.org/keywords/dihedral-angle","display_name":"Dihedral angle","score":0.5163975358009338},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.4428536891937256},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3708551228046417},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22221234440803528},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1336802840232849}],"concepts":[{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.6939274668693542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6587895154953003},{"id":"https://openalex.org/C2780392137","wikidata":"https://www.wikidata.org/wiki/Q17121801","display_name":"Ribbon","level":2,"score":0.6520676612854004},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6336148381233215},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5440492033958435},{"id":"https://openalex.org/C89025888","wikidata":"https://www.wikidata.org/wiki/Q911907","display_name":"Dihedral angle","level":4,"score":0.5163975358009338},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.4428536891937256},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3708551228046417},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22221234440803528},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1336802840232849},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"score":0.0},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C112887158","wikidata":"https://www.wikidata.org/wiki/Q169324","display_name":"Hydrogen bond","level":3,"score":0.0},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s00454-021-00287-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-021-00287-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-021-00287-3.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmid:34720305","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34720305","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & computational geometry","raw_type":null},{"id":"pmh:oai:arXiv.org:1611.10330","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.10330","pdf_url":"https://arxiv.org/pdf/1611.10330","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:scholarworks.smith.edu:mth_facpubs-1112","is_oa":true,"landing_page_url":"https://scholarworks.smith.edu/mth_facpubs/113","pdf_url":null,"source":{"id":"https://openalex.org/S4377196392","display_name":"Smith ScholarWorks (Smith College)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I202524275","host_organization_name":"Smith College","host_organization_lineage":["https://openalex.org/I202524275"],"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":"Mathematics and Statistics: Faculty Publications","raw_type":"text"},{"id":"pmh:oai:europepmc.org:7442671","is_oa":true,"landing_page_url":"http://europepmc.org/pmc/articles/PMC8550321","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8550321","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8550321","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Discrete Comput Geom","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00454-021-00287-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-021-00287-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-021-00287-3.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2896939856","display_name":null,"funder_award_id":"DMS 1821257","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4372618095","display_name":null,"funder_award_id":"SFARI","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G4674863495","display_name":null,"funder_award_id":"1821257","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6266353806","display_name":null,"funder_award_id":"1821212","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7814009930","display_name":null,"funder_award_id":"523862","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320315019","display_name":"Simons Foundation Autism Research Initiative","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2559432683.pdf"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W570602467","https://openalex.org/W1495116500","https://openalex.org/W1969646633","https://openalex.org/W1983284572","https://openalex.org/W1997771880","https://openalex.org/W2004748497","https://openalex.org/W2013122449","https://openalex.org/W2016305529","https://openalex.org/W2021711616","https://openalex.org/W2039884653","https://openalex.org/W2050495323","https://openalex.org/W2058587929","https://openalex.org/W2062400709","https://openalex.org/W2063663730","https://openalex.org/W2071586888","https://openalex.org/W2080878200","https://openalex.org/W2080972227","https://openalex.org/W2084990005","https://openalex.org/W2236053713","https://openalex.org/W2239511185","https://openalex.org/W2331691674","https://openalex.org/W2534220532","https://openalex.org/W2559432683","https://openalex.org/W2566362285","https://openalex.org/W2765384291","https://openalex.org/W2801697308","https://openalex.org/W2906517619","https://openalex.org/W2906743875","https://openalex.org/W2909131019","https://openalex.org/W3099570516","https://openalex.org/W3103800131","https://openalex.org/W3107424936","https://openalex.org/W3180662683","https://openalex.org/W4235281909","https://openalex.org/W4237981393","https://openalex.org/W4238099738","https://openalex.org/W4252289403"],"related_works":["https://openalex.org/W2128884622","https://openalex.org/W2112380088","https://openalex.org/W1715467939","https://openalex.org/W4318816969","https://openalex.org/W2067934601","https://openalex.org/W2161756346","https://openalex.org/W1977613337","https://openalex.org/W2075921262","https://openalex.org/W2300182960","https://openalex.org/W2796189570"],"abstract_inverted_index":{"Let":[0],"<i>M</i>":[1,40],"be":[2,93],"a":[3,37,54,71,88,117],"connected,":[4],"closed,":[5,66],"oriented":[6,14,67],"three-manifold":[7,68],"and":[8,32],"<i>K</i>,":[9],"<i>L</i>":[10,33],"two":[11],"rationally":[12],"null-homologous":[13],"simple":[15],"closed":[16],"curves":[17],"in":[18,34,81],"<i>M</i>.":[19],"We":[20],"give":[21],"an":[22,42],"explicit":[23],"algorithm":[24],"for":[25,87,109],"computing":[26],"the":[27,124],"linking":[28,79,103],"number":[29],"between":[30],"<i>K</i>":[31],"terms":[35],"of":[36,39,47,98],"presentation":[38],"as":[41],"irregular":[43],"dihedral":[44,96],"three-fold":[45],"cover":[46],"<mml:math":[48,56,90,99],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>S</mml:mi>":[49],"<mml:mn>3</mml:mn></mml:msup>":[50,60],"</mml:math>":[51,62],"branched":[52],"along":[53],"knot":[55,89],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>\u03b1</mml:mi>":[57],"<mml:mo>\u2282</mml:mo>":[58],"<mml:msup><mml:mi>S</mml:mi>":[59],"</mml:mrow>":[61],".":[63,101],"Since":[64],"every":[65],"admits":[69],"such":[70,112],"presentation,":[72],"our":[73],"results":[74],"apply":[75],"to":[76,123],"all":[77,82],"(well-defined)":[78],"numbers":[80,104],"three-manifolds.":[83],"Furthermore,":[84],"ribbon":[85],"obstructions":[86],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03b1</mml:mi></mml:math>":[91,100],"can":[92],"derived":[94],"from":[95],"covers":[97],"The":[102],"we":[105],"compute":[106],"are":[107],"necessary":[108],"evaluating":[110],"one":[111],"obstruction.":[113],"This":[114],"work":[115],"is":[116],"step":[118],"toward":[119],"testing":[120],"potential":[121],"counter-examples":[122],"Slice-Ribbon":[125],"Conjecture,":[126],"among":[127],"other":[128],"applications.":[129]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2021-07-19T00:00:00"}
