{"id":"https://openalex.org/W2748109384","doi":"https://doi.org/10.1080/10586458.2017.1422160","title":"Virtual Knot Cobordism and Bounding the Slice Genus","display_name":"Virtual Knot Cobordism and Bounding the Slice Genus","publication_year":2018,"publication_date":"2018-02-02","ids":{"openalex":"https://openalex.org/W2748109384","doi":"https://doi.org/10.1080/10586458.2017.1422160","mag":"2748109384"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2017.1422160","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1422160","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1708.05982","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120779428","display_name":"Hans Bod\u00e9n","orcid":"https://orcid.org/0000-0001-5516-8327"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Hans U. Boden","raw_affiliation_strings":["Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada","institution_ids":["https://openalex.org/I98251732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000102407","display_name":"Micah Chrisman","orcid":"https://orcid.org/0000-0001-7948-3436"},"institutions":[{"id":"https://openalex.org/I141450709","display_name":"Monmouth University","ror":"https://ror.org/01d6qxv05","country_code":"US","type":"education","lineage":["https://openalex.org/I141450709"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Micah Chrisman","raw_affiliation_strings":["Department of Mathematics, Monmouth University, West Long Branch, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Monmouth University, West Long Branch, NJ, USA","institution_ids":["https://openalex.org/I141450709"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040661297","display_name":"Robin Gaudreau","orcid":null},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Robin Gaudreau","raw_affiliation_strings":["Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada","institution_ids":["https://openalex.org/I98251732"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5120779428"],"corresponding_institution_ids":["https://openalex.org/I98251732"],"apc_list":null,"apc_paid":null,"fwci":4.1916,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.94251627,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"28","issue":"4","first_page":"475","last_page":"491"},"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/T11567","display_name":"semigroups and automata theory","score":0.9925000071525574,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.987500011920929,"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/mathematics","display_name":"Mathematics","score":0.8687900304794312},{"id":"https://openalex.org/keywords/cobordism","display_name":"Cobordism","score":0.8553088903427124},{"id":"https://openalex.org/keywords/knot","display_name":"Knot (papermaking)","score":0.7748711109161377},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.6098936200141907},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.5460690259933472},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39617013931274414},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32128965854644775},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13074588775634766},{"id":"https://openalex.org/keywords/botany","display_name":"Botany","score":0.1292283535003662},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09897881746292114},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07538282871246338}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8687900304794312},{"id":"https://openalex.org/C56213913","wikidata":"https://www.wikidata.org/wiki/Q2546666","display_name":"Cobordism","level":2,"score":0.8553088903427124},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.7748711109161377},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.6098936200141907},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.5460690259933472},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39617013931274414},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32128965854644775},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13074588775634766},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.1292283535003662},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09897881746292114},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07538282871246338},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10586458.2017.1422160","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1422160","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1708.05982","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.05982","pdf_url":"https://arxiv.org/pdf/1708.05982","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1708.05982","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.05982","pdf_url":"https://arxiv.org/pdf/1708.05982","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5349543763","display_name":null,"funder_award_id":"RGPIN-2016-05404","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W621627227","https://openalex.org/W1458607351","https://openalex.org/W1730928869","https://openalex.org/W1980367598","https://openalex.org/W1986653562","https://openalex.org/W1993137355","https://openalex.org/W2031367515","https://openalex.org/W2036216905","https://openalex.org/W2054563222","https://openalex.org/W2063945243","https://openalex.org/W2075869013","https://openalex.org/W2076104607","https://openalex.org/W2156613167","https://openalex.org/W2265212415","https://openalex.org/W2319156953","https://openalex.org/W2332709923","https://openalex.org/W2460645998","https://openalex.org/W2962786498","https://openalex.org/W2963169535","https://openalex.org/W2963694128","https://openalex.org/W2964299977","https://openalex.org/W3099767014","https://openalex.org/W3099993265","https://openalex.org/W3106058585"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4241539608","https://openalex.org/W4394644124","https://openalex.org/W2011909047","https://openalex.org/W4297786425","https://openalex.org/W2265375111","https://openalex.org/W2047441668","https://openalex.org/W2607394765","https://openalex.org/W4248818651","https://openalex.org/W282792582"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,15,53,75],"compute":[4],"the":[5,37,86],"slice":[6,72,87],"genus":[7,66,88],"for":[8],"many":[9,90],"low-crossing":[10],"virtual":[11,22,61,81,91],"knots.":[12],"For":[13],"instance,":[14],"show":[16,54],"that":[17,32,79],"1295":[18],"out":[19],"of":[20,36,48,60,89],"92,800":[21],"knots":[23,92],"with":[24,93],"six":[25,94],"or":[26,95],"fewer":[27,96],"crossings":[28],"are":[29,39,46],"slice,":[30],"and":[31,74],"all":[33],"but":[34],"248":[35],"rest":[38],"not":[40],"slice.":[41],"Key":[42],"to":[43,56,84],"these":[44],"results":[45],"computations":[47],"Turaev\u2019s":[49],"graded":[50,65],"genus,":[51],"which":[52],"extends":[55],"give":[57],"an":[58,77],"invariant":[59],"knot":[62],"concordance.":[63],"The":[64],"is":[67],"remarkably":[68],"effective":[69],"as":[70],"a":[71],"obstruction,":[73],"develop":[76],"algorithm":[78],"applies":[80],"unknotting":[82],"operations":[83],"determine":[85],"crossings.":[97]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3}],"updated_date":"2026-04-29T09:16:38.111599","created_date":"2025-10-10T00:00:00"}