{"id":"https://openalex.org/W346770570","doi":"https://doi.org/10.37236/4749","title":"Cataloguing PL 4-Manifolds by Gem-Complexity","display_name":"Cataloguing PL 4-Manifolds by Gem-Complexity","publication_year":2015,"publication_date":"2015-11-13","ids":{"openalex":"https://openalex.org/W346770570","doi":"https://doi.org/10.37236/4749","mag":"346770570"},"language":"en","primary_location":{"id":"doi:10.37236/4749","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4749","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p25/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p25/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070205249","display_name":"Massimiliano Casali","orcid":"https://orcid.org/0000-0003-3832-8696"},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Maria Rita Casali","raw_affiliation_strings":["University of Modena and Reggio Emilia (Italy)","University of Modena & Reggio Emilia, Italy"],"affiliations":[{"raw_affiliation_string":"University of Modena and Reggio Emilia (Italy)","institution_ids":["https://openalex.org/I122346577"]},{"raw_affiliation_string":"University of Modena & Reggio Emilia, Italy","institution_ids":["https://openalex.org/I122346577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018864330","display_name":"Paola Cristofori","orcid":"https://orcid.org/0000-0001-5531-8110"},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paola Cristofori","raw_affiliation_strings":["University of Modena and Reggio Emilia (Italy)","University of Modena & Reggio Emilia, Italy"],"affiliations":[{"raw_affiliation_string":"University of Modena and Reggio Emilia (Italy)","institution_ids":["https://openalex.org/I122346577"]},{"raw_affiliation_string":"University of Modena & Reggio Emilia, Italy","institution_ids":["https://openalex.org/I122346577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070205249"],"corresponding_institution_ids":["https://openalex.org/I122346577"],"apc_list":null,"apc_paid":null,"fwci":5.8166,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.96064054,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"22","issue":"4","first_page":null,"last_page":null},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9988999962806702,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7381674647331238},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.7248181104660034},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6870649456977844},{"id":"https://openalex.org/keywords/homeomorphism","display_name":"Homeomorphism (graph theory)","score":0.6237787008285522},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5766690969467163},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5429428219795227},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2027132511138916},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09124606847763062}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7381674647331238},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.7248181104660034},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6870649456977844},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.6237787008285522},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5766690969467163},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5429428219795227},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2027132511138916},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09124606847763062},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/4749","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4749","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p25/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/4749","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4749","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p25/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W346770570.pdf","grobid_xml":"https://content.openalex.org/works/W346770570.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W151486286","https://openalex.org/W286814258","https://openalex.org/W641322573","https://openalex.org/W653647932","https://openalex.org/W1497228321","https://openalex.org/W1572480646","https://openalex.org/W1597592613","https://openalex.org/W1618411552","https://openalex.org/W1620556779","https://openalex.org/W1693500505","https://openalex.org/W1723741009","https://openalex.org/W1834680130","https://openalex.org/W1966853340","https://openalex.org/W1967488681","https://openalex.org/W1984152820","https://openalex.org/W1988979552","https://openalex.org/W1990034619","https://openalex.org/W1990547276","https://openalex.org/W1990622099","https://openalex.org/W1992194225","https://openalex.org/W2000485416","https://openalex.org/W2010866194","https://openalex.org/W2012825852","https://openalex.org/W2017694782","https://openalex.org/W2020795286","https://openalex.org/W2022127071","https://openalex.org/W2033902599","https://openalex.org/W2034880833","https://openalex.org/W2041960293","https://openalex.org/W2043813208","https://openalex.org/W2045073296","https://openalex.org/W2049972599","https://openalex.org/W2056825190","https://openalex.org/W2062928624","https://openalex.org/W2067230975","https://openalex.org/W2090133103","https://openalex.org/W2096952305","https://openalex.org/W2105275999","https://openalex.org/W2115399178","https://openalex.org/W2126757328","https://openalex.org/W2169932795","https://openalex.org/W2283481147","https://openalex.org/W2522375474","https://openalex.org/W2755218945","https://openalex.org/W2945620251","https://openalex.org/W2949413409","https://openalex.org/W2949870377","https://openalex.org/W2952913285","https://openalex.org/W2963905120","https://openalex.org/W2964276759","https://openalex.org/W3097132297","https://openalex.org/W3101003962","https://openalex.org/W3106094400","https://openalex.org/W3106226189","https://openalex.org/W4234077252","https://openalex.org/W4235856277","https://openalex.org/W4238660434","https://openalex.org/W4246753030","https://openalex.org/W4294620451","https://openalex.org/W4298305762","https://openalex.org/W6620855012","https://openalex.org/W6647938356","https://openalex.org/W6980693108"],"related_works":["https://openalex.org/W1533075032","https://openalex.org/W2483809561","https://openalex.org/W3213871590","https://openalex.org/W4312038584","https://openalex.org/W812792805","https://openalex.org/W2362262239","https://openalex.org/W2951441447","https://openalex.org/W4301356681","https://openalex.org/W2168188726","https://openalex.org/W2090283050"],"abstract_inverted_index":{"We":[0],"describe":[1],"an":[2],"algorithm":[3],"to":[4,34,50,98,111],"subdivide":[5],"automatically":[6],"a":[7,56,83],"given":[8],"set":[9],"of":[10,43,86,93,105,114,117],"PL":[11,47,89,95],"$n$-manifolds":[12],"(via":[13],"coloured":[14,57],"triangulations":[15,116],"or,":[16],"equivalently,":[17],"via":[18],"crystallizations)":[19],"into":[20],"classes":[21],"whose":[22],"elements":[23],"are":[24,79,108],"PL-homeomorphic.":[25],"The":[26],"algorithm,":[27],"implemented":[28],"in":[29,74],"the":[30,37,41,66,87,91,106,118],"case":[31],"n=4,":[32],"succeeds":[33],"solve":[35],"completely":[36,68],"PL-homeomorphism":[38],"problem":[39],"among":[40,71],"catalogue":[42],"all":[44],"closed":[45],"connected":[46],"4-manifolds":[48,96],"up":[49,97],"gem-complexity":[51,99],"8":[52,100],"(i.e.,":[53],"which":[54],"admit":[55],"triangulation":[58],"with":[59,65],"at":[60],"most":[61],"18":[62],"4-simplices).Possible":[63],"interactions":[64],"(not":[67],"known)":[69],"relationship":[70],"different":[72,115],"classification":[73],"TOP":[75],"and":[76],"DIFF=PL":[77],"categories":[78],"also":[80],"investigated.":[81],"As":[82],"first":[84],"consequence":[85],"above":[88],"classification,":[90],"non-existence":[92],"exotic":[94],"is":[101],"proved.":[102],"Further":[103],"applications":[104],"tool":[107],"described,":[109],"related":[110],"possible":[112],"PL-recognition":[113],"K3-surface.":[119]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}