{"id":"https://openalex.org/W2001072494","doi":"https://doi.org/10.1080/10586458.2001.10504444","title":"Three-Manifolds Having Complexity At Most 9","display_name":"Three-Manifolds Having Complexity At Most 9","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2001072494","doi":"https://doi.org/10.1080/10586458.2001.10504444","mag":"2001072494"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2001.10504444","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504444","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":["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/A5054443284","display_name":"Bruno Martelli","orcid":"https://orcid.org/0000-0002-3664-7768"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]},{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Bruno Martelli","raw_affiliation_strings":["Dipartimento di Matematica , Universita di Firenze , Viale Morgagni 67a, 50134 , Firenze , Italy E-mail: martelli@math.unifi.it","Dipartimento di Matematica, Universit a di Firenze, Viale Morgagni 67a, 50134 Firenze, Italy","Dipartimento di Matematica Applicata, Universit a di Pisa, Via Bonanno Pisano 25/B 56126 Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica , Universita di Firenze , Viale Morgagni 67a, 50134 , Firenze , Italy E-mail: martelli@math.unifi.it","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Dipartimento di Matematica, Universit a di Firenze, Viale Morgagni 67a, 50134 Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Dipartimento di Matematica Applicata, Universit a di Pisa, Via Bonanno Pisano 25/B 56126 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038708897","display_name":"Carlo Petronio","orcid":"https://orcid.org/0000-0002-6067-2779"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carlo Petronio","raw_affiliation_strings":["Dipartimento di Matematica Applicata , Universit\u00e0 di Pisa , Via Bonanno Pisano 25/B, 56126 , Pisa , Italy E-mail: petronio@dm.unipi.it","Dipartimento di Matematica, Universit a di Firenze, Viale Morgagni 67a, 50134 Firenze, Italy","Dipartimento di Matematica Applicata, Universit a di Pisa, Via Bonanno Pisano 25/B 56126 Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica Applicata , Universit\u00e0 di Pisa , Via Bonanno Pisano 25/B, 56126 , Pisa , Italy E-mail: petronio@dm.unipi.it","institution_ids":["https://openalex.org/I108290504"]},{"raw_affiliation_string":"Dipartimento di Matematica, Universit a di Firenze, Viale Morgagni 67a, 50134 Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Dipartimento di Matematica Applicata, Universit a di Pisa, Via Bonanno Pisano 25/B 56126 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054443284"],"corresponding_institution_ids":["https://openalex.org/I108290504","https://openalex.org/I45084792"],"apc_list":null,"apc_paid":null,"fwci":7.1483,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.97697368,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"10","issue":"2","first_page":"207","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":1.0,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9995999932289124,"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":0.9990000128746033,"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":0.8388819694519043},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.6085547208786011},{"id":"https://openalex.org/keywords/3-manifold","display_name":"3-manifold","score":0.5948190689086914},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5932289361953735},{"id":"https://openalex.org/keywords/fibered-knot","display_name":"Fibered knot","score":0.5804500579833984},{"id":"https://openalex.org/keywords/hyperbolic-3-manifold","display_name":"Hyperbolic 3-manifold","score":0.5259316563606262},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5152862071990967},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.48117002844810486},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41679641604423523},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.3536655902862549},{"id":"https://openalex.org/keywords/relatively-hyperbolic-group","display_name":"Relatively hyperbolic group","score":0.28315049409866333},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27080872654914856},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12359640002250671},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11690637469291687}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8388819694519043},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.6085547208786011},{"id":"https://openalex.org/C191403955","wikidata":"https://www.wikidata.org/wiki/Q526901","display_name":"3-manifold","level":2,"score":0.5948190689086914},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5932289361953735},{"id":"https://openalex.org/C133776654","wikidata":"https://www.wikidata.org/wiki/Q2381352","display_name":"Fibered knot","level":2,"score":0.5804500579833984},{"id":"https://openalex.org/C129671197","wikidata":"https://www.wikidata.org/wiki/Q5957770","display_name":"Hyperbolic 3-manifold","level":5,"score":0.5259316563606262},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5152862071990967},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48117002844810486},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41679641604423523},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.3536655902862549},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.28315049409866333},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27080872654914856},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12359640002250671},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11690637469291687},{"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/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"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:10.1080/10586458.2001.10504444","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504444","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:CULeuclid:euclid.em/999188633","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/999188633","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1598737601","https://openalex.org/W1965191089","https://openalex.org/W2016418839","https://openalex.org/W2019558609","https://openalex.org/W2082573213","https://openalex.org/W2092265523"],"related_works":["https://openalex.org/W2126901807","https://openalex.org/W2963292905","https://openalex.org/W1975364308","https://openalex.org/W2013840997","https://openalex.org/W4301110675","https://openalex.org/W2035532951","https://openalex.org/W2771650160","https://openalex.org/W2950799516","https://openalex.org/W2245551571","https://openalex.org/W1649695420"],"abstract_inverted_index":{"We":[0,83],"describe":[1],"an":[2,89],"algorithm":[3,54],"which":[4,93],"has":[5],"enabled":[6],"us":[7],"to":[8,24,33,37,64,109],"give":[9,34],"a":[10,35],"complete":[11],"list,":[12],"without":[13],"repetitions,":[14],"of":[15,21,59,62,77,79,91,136],"all":[16],"closed":[17,122,133],"oriented":[18],"irreducible":[19],"three-manifolds":[20],"complexity":[22,63,110,126,144],"up":[23,108],"9.":[25,111],"More":[26],"interestingly,":[27],"we":[28,99],"have":[29],"actually":[30],"been":[31],"able":[32],"name":[36],"each":[38],"such":[39,81,106],"manifold,":[40],"by":[41,69],"recognizing":[42],"its":[43],"canonical":[44],"decomposition":[45],"into":[46],"Seifert":[47],"fibered":[48],"spaces":[49],"and":[50,73,98,128],"hyperbolic":[51,123,134],"manifolds.":[52,82,150],"The":[53],"relies":[55],"on":[56,74],"the":[57,65,75,131],"extension":[58],"Matveev's":[60],"theory":[61],"caseof":[66],"manifolds":[67,92,107,124,135,142],"bounded":[68],"suitably":[70],"marked":[71],"tori,":[72],"notion":[76],"assembling":[78,90],"two":[80],"show":[84],"that":[85,101,118],"every":[86],"manifold":[87],"is":[88,117],"cannot":[94],"be":[95],"further":[96],"disassembled,":[97],"prove":[100],"there":[102,119],"are":[103,120,130,148],"surprisingly":[104],"few":[105],"Our":[112],"most":[113,146],"interesting":[114],"experimental":[115],"discovery":[116],"4":[121,132],"having":[125,143],"9,":[127],"they":[129],"least":[137],"known":[138],"volume.":[139],"All":[140],"other":[141],"at":[145],"9":[147],"graph":[149]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}