{"id":"https://openalex.org/W2165079976","doi":"https://doi.org/10.1080/10586458.2006.10128965","title":"Computing Varieties of Representations of Hyperbolic 3-Manifolds into SL(4, \u211d)","display_name":"Computing Varieties of Representations of Hyperbolic 3-Manifolds into SL(4, \u211d)","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2165079976","doi":"https://doi.org/10.1080/10586458.2006.10128965","mag":"2165079976"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2006.10128965","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2006.10128965","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/A5109148669","display_name":"Daryl Cooper","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daryl Cooper","raw_affiliation_strings":["\n Department of Mathematics, University of California, Santa Barbara, CA 93106","Department of Mathematics, University of California, Santa Barbara, CA 93106"],"affiliations":[{"raw_affiliation_string":"\n Department of Mathematics, University of California, Santa Barbara, CA 93106","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Mathematics, University of California, Santa Barbara, CA 93106","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083901044","display_name":"D. D. Long","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Darren Long","raw_affiliation_strings":["\n Department of Mathematics, University of California, Santa Barbara, CA 93106","Department of Mathematics, University of California, Santa Barbara, CA 93106"],"affiliations":[{"raw_affiliation_string":"\n Department of Mathematics, University of California, Santa Barbara, CA 93106","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Mathematics, University of California, Santa Barbara, CA 93106","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029308543","display_name":"Morwen Thistlethwaite","orcid":"https://orcid.org/0000-0003-4890-0123"},"institutions":[{"id":"https://openalex.org/I2802706902","display_name":"Knoxville College","ror":"https://ror.org/02bxrp522","country_code":"US","type":"education","lineage":["https://openalex.org/I2802706902"]},{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Morwen Thistlethwaite","raw_affiliation_strings":["\n Department of Mathematics, University of Tennessee, Knoxville, TN 37996","Department of Mathematics, University of Tennessee, Knoxville, TN 37996"],"affiliations":[{"raw_affiliation_string":"\n Department of Mathematics, University of Tennessee, Knoxville, TN 37996","institution_ids":["https://openalex.org/I75027704","https://openalex.org/I2802706902"]},{"raw_affiliation_string":"Department of Mathematics, University of Tennessee, Knoxville, TN 37996","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109148669"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":0.8206,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.72742371,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"3","first_page":"291","last_page":"305"},"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":0.9937000274658203,"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":0.9868000149726868,"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":0.8471271395683289},{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.6989693641662598},{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.5931670069694519},{"id":"https://openalex.org/keywords/relatively-hyperbolic-group","display_name":"Relatively hyperbolic group","score":0.5862487554550171},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5816038846969604},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5384680032730103},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.531879723072052},{"id":"https://openalex.org/keywords/hyperbolic-group","display_name":"Hyperbolic group","score":0.5248342156410217},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.5112330913543701},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.4579445719718933},{"id":"https://openalex.org/keywords/fundamental-group","display_name":"Fundamental group","score":0.44587987661361694},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4263957738876343},{"id":"https://openalex.org/keywords/hyperbolic-3-manifold","display_name":"Hyperbolic 3-manifold","score":0.42402204871177673},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4140024781227112},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26604580879211426},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.20659300684928894},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.05855196714401245}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8471271395683289},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.6989693641662598},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.5931670069694519},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.5862487554550171},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5816038846969604},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5384680032730103},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.531879723072052},{"id":"https://openalex.org/C167150821","wikidata":"https://www.wikidata.org/wiki/Q81194","display_name":"Hyperbolic group","level":4,"score":0.5248342156410217},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.5112330913543701},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.4579445719718933},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.44587987661361694},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4263957738876343},{"id":"https://openalex.org/C129671197","wikidata":"https://www.wikidata.org/wiki/Q5957770","display_name":"Hyperbolic 3-manifold","level":5,"score":0.42402204871177673},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4140024781227112},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26604580879211426},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.20659300684928894},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.05855196714401245},{"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.2006.10128965","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2006.10128965","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5799999833106995,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1538177203","https://openalex.org/W1589886470","https://openalex.org/W1602669753","https://openalex.org/W1965191089","https://openalex.org/W2022365359","https://openalex.org/W2052596245","https://openalex.org/W2056721908","https://openalex.org/W2084036657","https://openalex.org/W2141040012","https://openalex.org/W2146796680","https://openalex.org/W2167801962","https://openalex.org/W2332288949","https://openalex.org/W2506123966","https://openalex.org/W3149442260"],"related_works":["https://openalex.org/W303677643","https://openalex.org/W2622280211","https://openalex.org/W4302192524","https://openalex.org/W2067549982","https://openalex.org/W2149889673","https://openalex.org/W4300893951","https://openalex.org/W2963292905","https://openalex.org/W2950811086","https://openalex.org/W4302084723","https://openalex.org/W3126100467"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"geometric":[2,122],"structure":[3,85],"on":[4],"a":[5,12,51,63,93],"closed":[6,67],"orientable":[7],"hyperbolic":[8,84],"3-":[9],"manifold":[10,114],"determines":[11],"discrete":[13],"faithful":[14],"representation":[15],"\u03c1":[16,44,76],"of":[17,43,47,66,121],"its":[18],"fundamental":[19],"group":[20],"into":[21,50,78],"SO+(3,":[22,48],"1),":[23],"unique":[24],"up":[25],"to":[26,39,92,112],"conjugacy.":[27],"Although":[28],"Mostow":[29],"rigidity":[30],"prohibits":[31],"us":[32],"from":[33],"deforming":[34],"\u03c1,":[35],"we":[36,57,100],"can":[37,86],"try":[38],"deform":[40],"the":[41,70,83,102,113],"composition":[42],"with":[45],"inclusion":[46],"1)":[49],"larger":[52],"group.":[53],"In":[54,97],"this":[55,98],"sense,":[56],"have":[58],"found":[59],"by":[60],"exact":[61],"computation":[62],"small":[64],"number":[65],"manifolds":[68],"in":[69,89],"Hodgson-":[71],"Weeks":[72],"census":[73],"for":[74,104],"which":[75],"deforms":[77],"SL(4,\u211d),":[79],"thus":[80],"showing":[81],"that":[82],"be":[87],"deformed":[88],"these":[90,106],"cases":[91],"real":[94],"projective":[95],"structure.":[96],"paper":[99],"describe":[101],"method":[103],"computing":[105],"deformations,":[107],"particular":[108],"attention":[109],"being":[110],"given":[111],"Vol3.":[115],"Keywords:":[116],"Primary":[117],"57M50Secondary":[118],"57-04Hyperbolic":[119],"3-manifoldsdeformation":[120],"structurealgorithms":[123]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}