{"id":"https://openalex.org/W4386317985","doi":"https://doi.org/10.1007/s00454-023-00539-4","title":"Arc Diagrams on 3-Manifold Spines","display_name":"Arc Diagrams on 3-Manifold Spines","publication_year":2023,"publication_date":"2023-08-31","ids":{"openalex":"https://openalex.org/W4386317985","doi":"https://doi.org/10.1007/s00454-023-00539-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-023-00539-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00539-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00539-4.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":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00539-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112806528","display_name":"Jack Brand","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Jack Brand","raw_affiliation_strings":["The Australian National University, Canberra, Australia"],"affiliations":[{"raw_affiliation_string":"The Australian National University, Canberra, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079605697","display_name":"Benjamin A. Burton","orcid":"https://orcid.org/0000-0002-3478-3301"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Benjamin A. Burton","raw_affiliation_strings":["The University of Queensland, St Lucia, Australia"],"affiliations":[{"raw_affiliation_string":"The University of Queensland, St Lucia, Australia","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041348558","display_name":"Zsuzsanna Dancso","orcid":"https://orcid.org/0000-0002-0598-3689"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Zsuzsanna Dancso","raw_affiliation_strings":["University of Sydney, Camperdown, Australia"],"affiliations":[{"raw_affiliation_string":"University of Sydney, Camperdown, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008902429","display_name":"Alexander He","orcid":"https://orcid.org/0000-0002-2189-4942"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Alexander He","raw_affiliation_strings":["The University of Queensland, St Lucia, Australia"],"affiliations":[{"raw_affiliation_string":"The University of Queensland, St Lucia, Australia","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038044019","display_name":"Adele Jackson","orcid":"https://orcid.org/0000-0002-8666-2827"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Adele Jackson","raw_affiliation_strings":["University of Oxford, Oxford, UK"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033291418","display_name":"Joan E. Licata","orcid":"https://orcid.org/0000-0003-4831-8563"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Joan Licata","raw_affiliation_strings":["The Australian National University, Canberra, Australia"],"affiliations":[{"raw_affiliation_string":"The Australian National University, Canberra, Australia","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5041348558"],"corresponding_institution_ids":["https://openalex.org/I129604602"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.1185,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7605497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"71","issue":"4","first_page":"1190","last_page":"1209"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.7158412337303162},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.5633026361465454},{"id":"https://openalex.org/keywords/link","display_name":"Link (geometry)","score":0.559114933013916},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5276783108711243},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5010135173797607},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4953433573246002},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.47415322065353394},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45738500356674194},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.45031100511550903},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.4397854208946228},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4239346981048584},{"id":"https://openalex.org/keywords/shadow","display_name":"Shadow (psychology)","score":0.422532320022583},{"id":"https://openalex.org/keywords/covering-space","display_name":"Covering space","score":0.41493356227874756},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3286636769771576},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19400665163993835},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17393618822097778},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09551918506622314},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05942538380622864}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7158412337303162},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.5633026361465454},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.559114933013916},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5276783108711243},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5010135173797607},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4953433573246002},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.47415322065353394},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45738500356674194},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.45031100511550903},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.4397854208946228},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4239346981048584},{"id":"https://openalex.org/C117797892","wikidata":"https://www.wikidata.org/wiki/Q286363","display_name":"Shadow (psychology)","level":2,"score":0.422532320022583},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.41493356227874756},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3286636769771576},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19400665163993835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17393618822097778},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09551918506622314},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05942538380622864},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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":1,"locations":[{"id":"doi:10.1007/s00454-023-00539-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00539-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00539-4.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"}],"best_oa_location":{"id":"doi:10.1007/s00454-023-00539-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00539-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00539-4.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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4099999964237213}],"awards":[],"funders":[{"id":"https://openalex.org/F4320309239","display_name":"Washburn University","ror":"https://ror.org/04sk2ar21"},{"id":"https://openalex.org/F4320315885","display_name":"Australian Government","ror":"https://ror.org/0314h5y94"},{"id":"https://openalex.org/F4320336183","display_name":"Clarendon Fund","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386317985.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1521147094","https://openalex.org/W1598737601","https://openalex.org/W1605569140","https://openalex.org/W1967586541","https://openalex.org/W1975401041","https://openalex.org/W1990472925","https://openalex.org/W2011801372","https://openalex.org/W2024087012","https://openalex.org/W2029233621","https://openalex.org/W2030834509","https://openalex.org/W2156613167","https://openalex.org/W2316343226","https://openalex.org/W2327745271","https://openalex.org/W2963527881","https://openalex.org/W2963627150","https://openalex.org/W2963810330","https://openalex.org/W4232140465"],"related_works":["https://openalex.org/W2893218741","https://openalex.org/W1518185400","https://openalex.org/W3200586296","https://openalex.org/W2558319350","https://openalex.org/W4230332972","https://openalex.org/W1492594177","https://openalex.org/W1998033311","https://openalex.org/W4247322236","https://openalex.org/W1842742976","https://openalex.org/W4231165741"],"abstract_inverted_index":{"Abstract":[0],"We":[1,13,32],"develop":[2],"a":[3,15,19,39,53,76,82],"theory":[4],"of":[5,11,21,29,55,81,84],"link":[6,37],"projections":[7,28],"to":[8,25,42,51,59,68],"trivalent":[9],"spines":[10],"3-manifolds.":[12],"prove":[14],"Reidemeister":[16],"Theorem":[17],"providing":[18],"set":[20,54],"combinatorial":[22,56],"moves":[23,57],"sufficient":[24,58],"relate":[26,60],"the":[27,66],"isotopic":[30],"links.":[31],"also":[33],"show":[34],"that":[35],"any":[36,43],"admits":[38],"crossingless":[40,61],"projection":[41],"special":[44],"spine":[45],"and":[46],"we":[47,64],"refine":[48],"our":[49,73],"theorem":[50],"provide":[52],"diagrams.":[62],"Finally,":[63],"discuss":[65],"connection":[67],"Turaev\u2019s":[69],"shadow":[70,79],"world,":[71],"interpreting":[72],"result":[74],"as":[75],"statement":[77],"about":[78],"equivalence":[80],"class":[83],"4-manifolds.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}
