{"id":"https://openalex.org/W2017446895","doi":"https://doi.org/10.1080/10586458.2008.10129044","title":"Commensurators of Cusped Hyperbolic Manifolds","display_name":"Commensurators of Cusped Hyperbolic Manifolds","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2017446895","doi":"https://doi.org/10.1080/10586458.2008.10129044","mag":"2017446895"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2008.10129044","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2008.10129044","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/A5062661455","display_name":"Oliver Goodman","orcid":null},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Oliver Goodman","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia","Department of Mathematics and Statistics, University of Melbourne, , Parkville, Victoria 3010, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Melbourne, , Parkville, Victoria 3010, Australia","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026219761","display_name":"Damian Heard","orcid":null},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Damian Heard","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia","Department of Mathematics and Statistics, University of Melbourne, , Parkville, Victoria 3010, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Melbourne, , Parkville, Victoria 3010, Australia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018902176","display_name":"Craig D. Hodgson","orcid":"https://orcid.org/0000-0002-3872-6822"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Craig Hodgson","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia","Department of Mathematics and Statistics, University of Melbourne, , Parkville, Victoria 3010, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Melbourne, , Parkville, Victoria 3010, Australia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062661455"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":3.5829,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.92209378,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"17","issue":"3","first_page":"283","last_page":"306"},"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":0.9945999979972839,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9873999953269958,"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":0.8900805711746216},{"id":"https://openalex.org/keywords/hyperbolic-3-manifold","display_name":"Hyperbolic 3-manifold","score":0.8687820434570312},{"id":"https://openalex.org/keywords/commensurability","display_name":"Commensurability (mathematics)","score":0.748934805393219},{"id":"https://openalex.org/keywords/hyperbolic-triangle","display_name":"Hyperbolic triangle","score":0.7013464570045471},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.6839682459831238},{"id":"https://openalex.org/keywords/ultraparallel-theorem","display_name":"Ultraparallel theorem","score":0.6652217507362366},{"id":"https://openalex.org/keywords/relatively-hyperbolic-group","display_name":"Relatively hyperbolic group","score":0.564659059047699},{"id":"https://openalex.org/keywords/hyperbolic-equilibrium-point","display_name":"Hyperbolic equilibrium point","score":0.5635257363319397},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.5422613620758057},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5114582777023315},{"id":"https://openalex.org/keywords/hyperbolic-group","display_name":"Hyperbolic group","score":0.5104953050613403},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.504883348941803},{"id":"https://openalex.org/keywords/hyperbolic-set","display_name":"Hyperbolic set","score":0.49633604288101196},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4932801127433777},{"id":"https://openalex.org/keywords/hyperbolic-coordinates","display_name":"Hyperbolic coordinates","score":0.4481187164783478},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.41470324993133545},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30157673358917236},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24810218811035156},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.19431152939796448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8900805711746216},{"id":"https://openalex.org/C129671197","wikidata":"https://www.wikidata.org/wiki/Q5957770","display_name":"Hyperbolic 3-manifold","level":5,"score":0.8687820434570312},{"id":"https://openalex.org/C119350121","wikidata":"https://www.wikidata.org/wiki/Q1091134","display_name":"Commensurability (mathematics)","level":2,"score":0.748934805393219},{"id":"https://openalex.org/C82673646","wikidata":"https://www.wikidata.org/wiki/Q2246553","display_name":"Hyperbolic triangle","level":4,"score":0.7013464570045471},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.6839682459831238},{"id":"https://openalex.org/C39308205","wikidata":"https://www.wikidata.org/wiki/Q7880612","display_name":"Ultraparallel theorem","level":5,"score":0.6652217507362366},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.564659059047699},{"id":"https://openalex.org/C51691630","wikidata":"https://www.wikidata.org/wiki/Q3925833","display_name":"Hyperbolic equilibrium point","level":4,"score":0.5635257363319397},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.5422613620758057},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5114582777023315},{"id":"https://openalex.org/C167150821","wikidata":"https://www.wikidata.org/wiki/Q81194","display_name":"Hyperbolic group","level":4,"score":0.5104953050613403},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.504883348941803},{"id":"https://openalex.org/C117855890","wikidata":"https://www.wikidata.org/wiki/Q3042004","display_name":"Hyperbolic set","level":2,"score":0.49633604288101196},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4932801127433777},{"id":"https://openalex.org/C55862258","wikidata":"https://www.wikidata.org/wiki/Q1017238","display_name":"Hyperbolic coordinates","level":5,"score":0.4481187164783478},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.41470324993133545},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30157673358917236},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24810218811035156},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.19431152939796448},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1080/10586458.2008.10129044","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2008.10129044","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/1227121383","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1227121383","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.245.181","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.245.181","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0801.4815v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.72.7228","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.72.7228","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ms.unimelb.edu.au/~snap/commens/commens.pdf","raw_type":"text"},{"id":"pmh:oai:jupiter.its.unimelb.edu.au:11343/29220","is_oa":false,"landing_page_url":"http://hdl.handle.net/11343/29220","pdf_url":null,"source":{"id":"https://openalex.org/S4377196259","display_name":"Minerva Access (University of Melbourne)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165779595","host_organization_name":"The University of Melbourne","host_organization_lineage":["https://openalex.org/I165779595"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1495308185","https://openalex.org/W1533061882","https://openalex.org/W1568953172","https://openalex.org/W1602669753","https://openalex.org/W1876922279","https://openalex.org/W1985307971","https://openalex.org/W1986803408","https://openalex.org/W2022365359","https://openalex.org/W2070913231","https://openalex.org/W2073270740","https://openalex.org/W2075872400","https://openalex.org/W2080546910","https://openalex.org/W2085585078","https://openalex.org/W2088793557","https://openalex.org/W2089010082","https://openalex.org/W2092609999","https://openalex.org/W2114785528","https://openalex.org/W2139839079","https://openalex.org/W2201503666","https://openalex.org/W2249240511","https://openalex.org/W2888943156","https://openalex.org/W3036468331","https://openalex.org/W3102359618","https://openalex.org/W3208026693"],"related_works":["https://openalex.org/W2207405255","https://openalex.org/W2951170829","https://openalex.org/W4300116253","https://openalex.org/W2030859484","https://openalex.org/W2608279773","https://openalex.org/W4301645415","https://openalex.org/W2350239503","https://openalex.org/W2465428195","https://openalex.org/W2017446895","https://openalex.org/W4322762869"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"a":[3,11],"general":[4],"algorithm":[5,64],"for":[6,18,94],"finding":[7],"the":[8,48,58,63,78,95],"commensurator":[9],"of":[10,50,81,97],"nonarithmetic":[12,52],"hyperbolic":[13,53,61,84,98],"manifold":[14],"with":[15,102],"cusps":[16],"and":[17,37,93,100],"deciding":[19],"when":[20],"two":[21],"such":[22],"manifolds":[23],"are":[24],"commensurable.":[25],"The":[26],"method":[27],"is":[28],"based":[29],"on":[30],"some":[31],"elementary":[32],"observations":[33],"regarding":[34],"horosphere":[35],"packings":[36],"canonical":[38],"cell":[39],"decompositions.":[40],"For":[41,60],"example,":[42],"we":[43],"use":[44,74],"this":[45,75],"to":[46,76,104],"find":[47],"commensurators":[49],"all":[51,82],"once-punctured":[54],"torus":[55],"bundles":[56],"over":[57],"circle.":[59],"3-manifolds,":[62],"has":[65],"been":[66],"implemented":[67],"using":[68,87],"Goodman's":[69],"computer":[70],"program":[71],"Snap.":[72],"We":[73],"determine":[77],"commensurability":[79],"classes":[80],"cusped":[83],"3-manifolds":[85],"triangulated":[86],"at":[88],"most":[89],"seven":[90],"ideal":[91],"tetrahedra,":[92],"complements":[96],"knots":[99],"links":[101],"up":[103],"twelve":[105],"crossings.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
