{"id":"https://openalex.org/W2044720368","doi":"https://doi.org/10.1090/s0273-0979-1982-15003-0","title":"Three dimensional manifolds, Kleinian groups and hyperbolic geometry","display_name":"Three dimensional manifolds, Kleinian groups and hyperbolic geometry","publication_year":1982,"publication_date":"1982-05-01","ids":{"openalex":"https://openalex.org/W2044720368","doi":"https://doi.org/10.1090/s0273-0979-1982-15003-0","mag":"2044720368"},"language":"en","primary_location":{"id":"doi:10.1090/s0273-0979-1982-15003-0","doi":"https://doi.org/10.1090/s0273-0979-1982-15003-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0273-0979-1982-15003-0","pdf_url":"https://www.ams.org/bull/1982-06-03/S0273-0979-1982-15003-0/S0273-0979-1982-15003-0.pdf","source":{"id":"https://openalex.org/S71584477","display_name":"Bulletin of the American Mathematical Society","issn_l":"0002-9904","issn":["0002-9904","0273-0979","1088-9485","1936-881X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.ams.org/bull/1982-06-03/S0273-0979-1982-15003-0/S0273-0979-1982-15003-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040489403","display_name":"William P.HG Thurston","orcid":"https://orcid.org/0000-0003-4157-517X","observed_orcids":["https://orcid.org/0000-0003-4157-517X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"William P. Thurston","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5040489403"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":21.0296,"has_fulltext":true,"cited_by_count":1319,"citation_normalized_percentile":{"value":0.99939431,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"6","issue":"3","first_page":"357","last_page":"382"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9911999702453613,"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":0.9911999702453613,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.001500000013038516,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/3-manifolds","display_name":"3-manifolds","score":0.8299999833106995},{"id":"https://openalex.org/keywords/kleinian-groups","display_name":"Kleinian groups","score":0.9890000224113464},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"hyperbolic geometry","score":0.9990000128746033},{"id":"https://openalex.org/keywords/hyperbolic-3-manifolds","display_name":"hyperbolic 3-manifolds","score":0.9079999923706055},{"id":"https://openalex.org/keywords/riemann-surfaces","display_name":"Riemann surfaces","score":0.8429999947547913},{"id":"https://openalex.org/keywords/constant-curvature-metrics","display_name":"constant curvature metrics","score":0.671999990940094},{"id":"https://openalex.org/keywords/poincare-conjecture","display_name":"Poincar\u00e9 conjecture","score":0.8220000267028809}],"concepts":[{"id":"https://openalex.org/C49527426","wikidata":"https://www.wikidata.org/wiki/Q4116484","display_name":"Kleinian group","level":2,"score":0.8072866797447205},{"id":"https://openalex.org/C129671197","wikidata":"https://www.wikidata.org/wiki/Q5957770","display_name":"Hyperbolic 3-manifold","level":5,"score":0.6910676956176758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6820155382156372},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.46673616766929626},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4440957307815552},{"id":"https://openalex.org/C82673646","wikidata":"https://www.wikidata.org/wiki/Q2246553","display_name":"Hyperbolic triangle","level":4,"score":0.44137153029441833},{"id":"https://openalex.org/C167150821","wikidata":"https://www.wikidata.org/wiki/Q81194","display_name":"Hyperbolic group","level":4,"score":0.4131774306297302},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.39038801193237305},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36147743463516235},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3273320198059082},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.23479041457176208},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.20225727558135986}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0273-0979-1982-15003-0","doi":"https://doi.org/10.1090/s0273-0979-1982-15003-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0273-0979-1982-15003-0","pdf_url":"https://www.ams.org/bull/1982-06-03/S0273-0979-1982-15003-0/S0273-0979-1982-15003-0.pdf","source":{"id":"https://openalex.org/S71584477","display_name":"Bulletin of the American Mathematical Society","issn_l":"0002-9904","issn":["0002-9904","0273-0979","1088-9485","1936-881X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of the American Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.535.7618","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.535.7618","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csee.wvu.edu/~xinl/library/papers/math/geometry/thurston1982.pdf","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.bams/1183548782","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bams/1183548782","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,"listed_in":[],"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":{"id":"doi:10.1090/s0273-0979-1982-15003-0","doi":"https://doi.org/10.1090/s0273-0979-1982-15003-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0273-0979-1982-15003-0","pdf_url":"https://www.ams.org/bull/1982-06-03/S0273-0979-1982-15003-0/S0273-0979-1982-15003-0.pdf","source":{"id":"https://openalex.org/S71584477","display_name":"Bulletin of the American Mathematical Society","issn_l":"0002-9904","issn":["0002-9904","0273-0979","1088-9485","1936-881X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2044720368.pdf","grobid_xml":"https://content.openalex.org/works/W2044720368.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W578133573","https://openalex.org/W1486462508","https://openalex.org/W1550283619","https://openalex.org/W1965565198","https://openalex.org/W1967759674","https://openalex.org/W1980585398","https://openalex.org/W2002902707","https://openalex.org/W2067880356","https://openalex.org/W2075529902","https://openalex.org/W2084633334","https://openalex.org/W2084641659","https://openalex.org/W2127020756","https://openalex.org/W2136209605","https://openalex.org/W2147134403","https://openalex.org/W2169194620","https://openalex.org/W2318517541","https://openalex.org/W2326413593","https://openalex.org/W2566412846","https://openalex.org/W2610251645","https://openalex.org/W4295689515","https://openalex.org/W6605591553","https://openalex.org/W6819002306"],"related_works":["https://openalex.org/W7099997146","https://openalex.org/W2011174315","https://openalex.org/W2496339678","https://openalex.org/W1966331339","https://openalex.org/W87354914","https://openalex.org/W2078057192","https://openalex.org/W7100642523","https://openalex.org/W7095472642","https://openalex.org/W7097712902","https://openalex.org/W4287552980"],"abstract_inverted_index":{"1.":[0],"A":[1,6],"conjectural":[2],"picture":[3],"of":[4,9,45,52,89,97,141],"3-manifolds.":[5],"major":[7],"thrust":[8],"mathematics":[10],"in":[11,16,70,78,166],"the":[12,24,49,71,79,83,87,90,102,105,148,168],"late":[13],"19th":[14],"century,":[15],"which":[17],"Poincare":[18],"had":[19],"a":[20,35,42,61,64,76,94],"large":[21],"role,":[22],"was":[23,131],"uniformization":[25],"theory":[26,138],"for":[27,139,147],"Riemann":[28],"surfaces:":[29],"that":[30,127,150,161],"every":[31],"conformai":[32],"structure":[33],"on":[34],"closed":[36],"oriented":[37],"surface":[38,72,84],"is":[39,73,86,123],"represented":[40],"by":[41,93],"Riemannian":[43],"metric":[44,62],"constant":[46],"curvature.":[47],"For":[48],"typical":[50],"case":[51],"negative":[53],"Euler":[54],"characteristic":[55],"(genus":[56],"greater":[57],"than":[58,117],"1)":[59],"such":[60],"gives":[63],"hyperbolic":[65,80,91],"structure:":[66],"any":[67,136],"small":[68],"neighborhood":[69,77],"isometric":[74],"to":[75,125,134],"plane,":[81],"and":[82,104,109,119],"itself":[85],"quotient":[88],"plane":[92],"discrete":[95],"group":[96],"motions.":[98],"The":[99,156],"exceptional":[100],"cases,":[101],"sphere":[103],"torus,":[106],"have":[107],"spherical":[108],"Euclidean":[110],"structures.":[111],"Three-manifolds":[112],"are":[113,154],"greatly":[114],"more":[115],"complicated":[116],"surfaces,":[118],"I":[120,162],"think":[121],"it":[122],"fair":[124],"say":[126],"until":[128],"recently":[129],"there":[130],"little":[132],"reason":[133],"expect":[135],"analogous":[137],"manifolds":[140],"dimension":[142],"3":[143],"(or":[144],"more)\u2014except":[145],"perhaps":[146],"fact":[149],"so":[151,160],"many":[152],"3-manifolds":[153],"beautiful.":[155],"situation":[157],"has":[158],"changed,":[159],"feel":[163],"fairly":[164],"confident":[165],"proposing":[167]},"counts_by_year":[{"year":2026,"cited_by_count":32},{"year":2025,"cited_by_count":40},{"year":2024,"cited_by_count":27},{"year":2023,"cited_by_count":35},{"year":2022,"cited_by_count":34},{"year":2021,"cited_by_count":53},{"year":2020,"cited_by_count":43},{"year":2019,"cited_by_count":48},{"year":2018,"cited_by_count":28},{"year":2017,"cited_by_count":23},{"year":2016,"cited_by_count":44},{"year":2015,"cited_by_count":43},{"year":2014,"cited_by_count":47},{"year":2013,"cited_by_count":36},{"year":2012,"cited_by_count":34}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}