{"id":"https://openalex.org/W4245261811","doi":"https://doi.org/10.1109/visual.2005.1532843","title":"Visualization of the Genus of Knots","display_name":"Visualization of the Genus of Knots","publication_year":2006,"publication_date":"2006-10-11","ids":{"openalex":"https://openalex.org/W4245261811","doi":"https://doi.org/10.1109/visual.2005.1532843"},"language":"en","primary_location":{"id":"doi:10.1109/visual.2005.1532843","is_oa":false,"landing_page_url":"https://doi.org/10.1109/visual.2005.1532843","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VIS 05. IEEE Visualization, 2005.","raw_type":"proceedings-article"},"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/A5040153657","display_name":"J.J. van Wijk","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"J.J. van Wijk","raw_affiliation_strings":["Department Mathematics and Computer Science, Technische Universiteit Eindhoven, Netherlands"],"affiliations":[{"raw_affiliation_string":"Department Mathematics and Computer Science, Technische Universiteit Eindhoven, Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084882214","display_name":"A.M. Cohen","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"A.M. Cohen","raw_affiliation_strings":["Department Mathematics and Computer Science, Technische Universiteit Eindhoven, Netherlands"],"affiliations":[{"raw_affiliation_string":"Department Mathematics and Computer Science, Technische Universiteit Eindhoven, Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040153657"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":null,"apc_paid":null,"fwci":0.4253,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66140481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"567","last_page":"574"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9933000206947327,"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":0.9933000206947327,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9793999791145325,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/knot","display_name":"Knot (papermaking)","score":0.8290305137634277},{"id":"https://openalex.org/keywords/seifert-surface","display_name":"Seifert surface","score":0.683885395526886},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.5991560220718384},{"id":"https://openalex.org/keywords/braid","display_name":"Braid","score":0.5817551612854004},{"id":"https://openalex.org/keywords/knot-theory","display_name":"Knot theory","score":0.5737334489822388},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4566057026386261},{"id":"https://openalex.org/keywords/knot-invariant","display_name":"Knot invariant","score":0.4293370842933655},{"id":"https://openalex.org/keywords/schematic","display_name":"Schematic","score":0.42590320110321045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33833885192871094},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1743643879890442},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.08832469582557678},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.061878204345703125}],"concepts":[{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.8290305137634277},{"id":"https://openalex.org/C173628569","wikidata":"https://www.wikidata.org/wiki/Q1554293","display_name":"Seifert surface","level":5,"score":0.683885395526886},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.5991560220718384},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.5817551612854004},{"id":"https://openalex.org/C143330242","wikidata":"https://www.wikidata.org/wiki/Q849798","display_name":"Knot theory","level":3,"score":0.5737334489822388},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4566057026386261},{"id":"https://openalex.org/C36794415","wikidata":"https://www.wikidata.org/wiki/Q1862434","display_name":"Knot invariant","level":4,"score":0.4293370842933655},{"id":"https://openalex.org/C192328126","wikidata":"https://www.wikidata.org/wiki/Q4514647","display_name":"Schematic","level":2,"score":0.42590320110321045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33833885192871094},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1743643879890442},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.08832469582557678},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.061878204345703125},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/visual.2005.1532843","is_oa":false,"landing_page_url":"https://doi.org/10.1109/visual.2005.1532843","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VIS 05. IEEE Visualization, 2005.","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.tue.nl:publications/2f0e9f7d-14ed-4bca-909a-36c1aaa1bd8f","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/2f0e9f7d-14ed-4bca-909a-36c1aaa1bd8f","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Wijk, van, J J & Cohen, A M 2005, Visualization of the genus of knots. in C Silva, E Gr\u00f6ller & H Rushmeier (eds), Proceedings IEEE Visualization 2005 (Minneapolis MN, USA, October 23-28, 2005). Institute of Electrical and Electronics Engineers, pp. 567-574. https://doi.org/10.1109/VISUAL.2005.1532843","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/2f0e9f7d-14ed-4bca-909a-36c1aaa1bd8f","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/2f0e9f7d-14ed-4bca-909a-36c1aaa1bd8f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings IEEE Visualization 2005 (Minneapolis MN, USA, October 23-28, 2005), 567 - 574","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1847044884","https://openalex.org/W2032325716","https://openalex.org/W2053383972","https://openalex.org/W2068489447","https://openalex.org/W4233106844","https://openalex.org/W4299992305","https://openalex.org/W6636375265","https://openalex.org/W7010866536","https://openalex.org/W7066893122"],"related_works":["https://openalex.org/W1495779939","https://openalex.org/W2900994935","https://openalex.org/W2753977118","https://openalex.org/W2892680669","https://openalex.org/W3101283995","https://openalex.org/W2793606861","https://openalex.org/W1622356303","https://openalex.org/W4362473285","https://openalex.org/W2107691367","https://openalex.org/W588098128"],"abstract_inverted_index":{"The":[0],"genus":[1,125],"of":[2,16,35,64,77,123,126],"a":[3,17,120,127],"knot":[4,18,30,45,103,109],"or":[5,19,31],"link":[6,20],"can":[7,97],"be":[8,98],"defined":[9],"via":[10],"Seifert":[11,14],"surfaces.":[12],"A":[13,69],"surface":[15,24,112],"is":[21,51,67,71,91,104],"an":[22],"oriented":[23,95],"whose":[25],"boundary":[26],"coincides":[27],"with":[28],"that,":[29],"link.":[32],"Schematic":[33],"images":[34],"these":[36,49],"surfaces":[37,66,78,96,118],"are":[38],"shown":[39,92],"in":[40,100],"every":[41],"text":[42],"book":[43],"on":[44],"theory,":[46],"but":[47],"from":[48,84],"it":[50,90],"hard":[52],"to":[53,73],"understand":[54],"their":[55],"shape":[56],"and":[57,81],"structure.":[58],"In":[59],"this":[60],"paper":[61],"the":[62,85,102,108,111,124],"visualization":[63,122],"such":[65,106],"discussed.":[68],"method":[70],"presented":[72],"produce":[74],"different":[75],"styles":[76],"for":[79],"knots":[80],"links,":[82],"starting":[83],"so-called":[86],"braid":[87],"representation.":[88],"Also,":[89],"how":[93],"closed":[94,117],"generated":[99],"which":[101],"embedded,":[105],"that":[107],"subdivides":[110],"into":[113],"two":[114],"parts.":[115],"These":[116],"provide":[119],"direct":[121],"knot.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}