{"id":"https://openalex.org/W1998475337","doi":"https://doi.org/10.1142/s0218216500000293","title":"VIRTUAL KNOT PRESENTATION OF RIBBON TORUS-KNOTS","display_name":"VIRTUAL KNOT PRESENTATION OF RIBBON TORUS-KNOTS","publication_year":2000,"publication_date":"2000-06-01","ids":{"openalex":"https://openalex.org/W1998475337","doi":"https://doi.org/10.1142/s0218216500000293","mag":"1998475337"},"language":"en","primary_location":{"id":"doi:10.1142/s0218216500000293","doi":"https://doi.org/10.1142/s0218216500000293","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218216500000293","pdf_url":null,"source":{"id":"https://openalex.org/S55337115","display_name":"Journal of Knot Theory and Its Ramifications","issn_l":"0218-2165","issn":["0218-2165","1793-6527"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-4"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Knot Theory and Its Ramifications","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060507525","display_name":"Shin Satoh","orcid":"https://orcid.org/0000-0002-4918-3683","observed_orcids":["https://orcid.org/0000-0002-4918-3683"]},"institutions":[{"id":"https://openalex.org/I317356780","display_name":"Osaka City University","ror":"https://ror.org/02skfsw40","country_code":"JP","type":"education","lineage":["https://openalex.org/I317356780","https://openalex.org/I4387152983"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"SHIN SATOH","raw_affiliation_strings":["Department of Mathematics, Osaka City University, Sumiyoshi, Osaka 558-8585, Japan","Department of Mathematics, Osaka City University, Sumiyoshi, Osaka 558 8585, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Osaka City University, Sumiyoshi, Osaka 558-8585, Japan","institution_ids":["https://openalex.org/I317356780"]},{"raw_affiliation_string":"Department of Mathematics, Osaka City University, Sumiyoshi, Osaka 558 8585, Japan","institution_ids":["https://openalex.org/I317356780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060507525"],"corresponding_institution_ids":["https://openalex.org/I317356780"],"apc_list":null,"apc_paid":null,"fwci":3.7579,"has_fulltext":false,"cited_by_count":112,"citation_normalized_percentile":{"value":0.92470617,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"09","issue":"04","first_page":"531","last_page":"542"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.0,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0,"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/virtual-knots","display_name":"virtual knots","score":0.9919999837875366},{"id":"https://openalex.org/keywords/4-manifold-topology","display_name":"4-manifold topology","score":0.5960000157356262},{"id":"https://openalex.org/keywords/knot-groups","display_name":"knot groups","score":0.5799999833106995}],"concepts":[{"id":"https://openalex.org/C2780392137","wikidata":"https://www.wikidata.org/wiki/Q17121801","display_name":"Ribbon","level":2,"score":0.8841766119003296},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7810245752334595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.741256833076477},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.6447892785072327},{"id":"https://openalex.org/C129946241","wikidata":"https://www.wikidata.org/wiki/Q1634206","display_name":"Alexander polynomial","level":4,"score":0.6211948990821838},{"id":"https://openalex.org/C143330242","wikidata":"https://www.wikidata.org/wiki/Q849798","display_name":"Knot theory","level":3,"score":0.5319103598594666},{"id":"https://openalex.org/C19794929","wikidata":"https://www.wikidata.org/wiki/Q168620","display_name":"Trefoil knot","level":4,"score":0.4955674409866333},{"id":"https://openalex.org/C36794415","wikidata":"https://www.wikidata.org/wiki/Q1862434","display_name":"Knot invariant","level":4,"score":0.4679265022277832},{"id":"https://openalex.org/C180837527","wikidata":"https://www.wikidata.org/wiki/Q7841270","display_name":"Tricolorability","level":5,"score":0.46764373779296875},{"id":"https://openalex.org/C58666742","wikidata":"https://www.wikidata.org/wiki/Q4421793","display_name":"Skein relation","level":4,"score":0.4174971282482147},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3721880614757538},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3716496229171753},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2904523015022278},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.05223223567008972},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218216500000293","doi":"https://doi.org/10.1142/s0218216500000293","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218216500000293","pdf_url":null,"source":{"id":"https://openalex.org/S55337115","display_name":"Journal of Knot Theory and Its Ramifications","issn_l":"0218-2165","issn":["0218-2165","1793-6527"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-4"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Knot Theory and Its Ramifications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1539598332","https://openalex.org/W1575957258","https://openalex.org/W2052810629","https://openalex.org/W2113182425","https://openalex.org/W2156613167","https://openalex.org/W2314804202"],"related_works":["https://openalex.org/W2944398340","https://openalex.org/W1965458078","https://openalex.org/W2001601711","https://openalex.org/W2305647332","https://openalex.org/W2952464068","https://openalex.org/W2081196071","https://openalex.org/W2954316213","https://openalex.org/W1982211104","https://openalex.org/W2796768140","https://openalex.org/W3104344644"],"abstract_inverted_index":{"Any":[0],"ribbon":[1,17],"torus-knot":[2],"in":[3],"4-space":[4],"is":[5],"naturally":[6],"associated":[7],"with":[8],"a":[9,14,28,32],"virtual":[10,20,34],"knot.":[11],"We":[12,25],"investigate":[13],"relationship":[15],"between":[16],"torus-knots":[18],"and":[19,44],"knots":[21,35],"from":[22],"this":[23],"viewpoint.":[24],"also":[26],"give":[27],"new":[29],"example":[30],"of":[31],"non-classical":[33],"which":[36],"can":[37],"not":[38],"be":[39],"detected":[40],"by":[41],"the":[42,45],"group":[43],"Z-polynomial.":[46]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
