{"id":"https://openalex.org/W1991311317","doi":"https://doi.org/10.1142/s0218196704001682","title":"FREELY INDECOMPOSABLE GROUPS ACTING ON HYPERBOLIC SPACES","display_name":"FREELY INDECOMPOSABLE GROUPS ACTING ON HYPERBOLIC SPACES","publication_year":2004,"publication_date":"2004-04-01","ids":{"openalex":"https://openalex.org/W1991311317","doi":"https://doi.org/10.1142/s0218196704001682","mag":"1991311317"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196704001682","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196704001682","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5023281472","display_name":"Ilya Kapovich","orcid":"https://orcid.org/0000-0002-7694-6236"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"ILYA KAPOVICH","raw_affiliation_strings":["Deparment of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA"],"affiliations":[{"raw_affiliation_string":"Deparment of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035673859","display_name":"Richard Weidmann","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"RICHARD WEIDMANN","raw_affiliation_strings":["Department of Mathematics, Johann Wolfgang Goethe University, Robert Mayer Strasse 6\u20138, 60325 Frankfurt, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Johann Wolfgang Goethe University, Robert Mayer Strasse 6\u20138, 60325 Frankfurt, Germany","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023281472"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":2.9028,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.90057722,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"02","first_page":"115","last_page":"171"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.996399998664856,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9962000250816345,"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":0.9375770092010498},{"id":"https://openalex.org/keywords/quasiconvex-function","display_name":"Quasiconvex function","score":0.8280024528503418},{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.7439154386520386},{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.7154146432876587},{"id":"https://openalex.org/keywords/relatively-hyperbolic-group","display_name":"Relatively hyperbolic group","score":0.6966214179992676},{"id":"https://openalex.org/keywords/hyperbolic-group","display_name":"Hyperbolic group","score":0.6354177594184875},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6302798986434937},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.593194842338562},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.4559115171432495},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.19552448391914368},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16568443179130554},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.14232730865478516},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09407055377960205},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.06044468283653259}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9375770092010498},{"id":"https://openalex.org/C80278974","wikidata":"https://www.wikidata.org/wiki/Q1126412","display_name":"Quasiconvex function","level":5,"score":0.8280024528503418},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.7439154386520386},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.7154146432876587},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.6966214179992676},{"id":"https://openalex.org/C167150821","wikidata":"https://www.wikidata.org/wiki/Q81194","display_name":"Hyperbolic group","level":4,"score":0.6354177594184875},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6302798986434937},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.593194842338562},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.4559115171432495},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.19552448391914368},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16568443179130554},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.14232730865478516},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09407055377960205},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.06044468283653259},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.0},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196704001682","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196704001682","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W198698382","https://openalex.org/W611098039","https://openalex.org/W1234885875","https://openalex.org/W1516116134","https://openalex.org/W1523645334","https://openalex.org/W1545078593","https://openalex.org/W1571539704","https://openalex.org/W1589886470","https://openalex.org/W1641192973","https://openalex.org/W1909362234","https://openalex.org/W1927956358","https://openalex.org/W1967512719","https://openalex.org/W1977589901","https://openalex.org/W2001355211","https://openalex.org/W2005237754","https://openalex.org/W2029354991","https://openalex.org/W2040960421","https://openalex.org/W2044092288","https://openalex.org/W2047968009","https://openalex.org/W2065245802","https://openalex.org/W2072112282","https://openalex.org/W2083670277","https://openalex.org/W2086003047","https://openalex.org/W2086991489","https://openalex.org/W2092160535","https://openalex.org/W2113413876","https://openalex.org/W2122013186","https://openalex.org/W2130222180","https://openalex.org/W2134086356","https://openalex.org/W2134309556","https://openalex.org/W2135746084","https://openalex.org/W2152237026","https://openalex.org/W2160742274","https://openalex.org/W2318910871","https://openalex.org/W2321615784","https://openalex.org/W2327672643","https://openalex.org/W2394548822","https://openalex.org/W2998190715","https://openalex.org/W3194331646","https://openalex.org/W4292101339","https://openalex.org/W6605483616"],"related_works":["https://openalex.org/W2622280211","https://openalex.org/W4302192524","https://openalex.org/W4301122216","https://openalex.org/W4294294477","https://openalex.org/W2785555998","https://openalex.org/W2149889673","https://openalex.org/W2953201955","https://openalex.org/W2950163392","https://openalex.org/W2081281167","https://openalex.org/W2936331589"],"abstract_inverted_index":{"We":[0],"obtain":[1],"a":[2,18],"number":[3],"of":[4,30],"finiteness":[5],"results":[6],"for":[7],"groups":[8],"acting":[9],"on":[10],"Gromov-hyperbolic":[11],"spaces.":[12],"In":[13],"particular":[14],"we":[15],"show":[16],"that":[17],"torsion-free":[19],"locally":[20],"quasiconvex":[21],"hyperbolic":[22],"group":[23],"has":[24],"only":[25],"finitely":[26],"many":[27],"conjugacy":[28],"classes":[29],"n-generated":[31],"one-ended":[32],"subgroups.":[33]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}