{"id":"https://openalex.org/W1671388533","doi":"https://doi.org/10.1142/s0218196715500289","title":"Groups acting on hyperbolic \u039b-metric spaces","display_name":"Groups acting on hyperbolic \u039b-metric spaces","publication_year":2015,"publication_date":"2015-07-20","ids":{"openalex":"https://openalex.org/W1671388533","doi":"https://doi.org/10.1142/s0218196715500289","mag":"1671388533"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196715500289","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715500289","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1310.4882","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Andrei-Paul Grecianu","orcid":null},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andrei-Paul Grecianu","raw_affiliation_strings":["Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA"],"affiliations":[{"raw_affiliation_string":"Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Alexei V. Kvaschuk","orcid":null},"institutions":[{"id":"https://openalex.org/I100621029","display_name":"Bank of America","ror":"https://ror.org/006tvg625","country_code":"US","type":"other","lineage":["https://openalex.org/I100621029"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexei V. Kvaschuk","raw_affiliation_strings":["Bank of America Corporate Center, 100 N Tryon St, Charlotte, North Carolina 28255, USA"],"affiliations":[{"raw_affiliation_string":"Bank of America Corporate Center, 100 N Tryon St, Charlotte, North Carolina 28255, USA","institution_ids":["https://openalex.org/I100621029"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Alexei G. Myasnikov","orcid":null},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexei G. Myasnikov","raw_affiliation_strings":["Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA"],"affiliations":[{"raw_affiliation_string":"Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"last","author":{"id":null,"display_name":"Denis E. Serbin","orcid":null},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Denis E. Serbin","raw_affiliation_strings":["Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA"],"affiliations":[{"raw_affiliation_string":"Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA","institution_ids":["https://openalex.org/I108468826"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I108468826"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.04044118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"25","issue":"06","first_page":"977","last_page":"1042"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.262800008058548,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.262800008058548,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.11190000176429749,"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":0.10419999808073044,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6245999932289124},{"id":"https://openalex.org/keywords/relatively-hyperbolic-group","display_name":"Relatively hyperbolic group","score":0.5896000266075134},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5748000144958496},{"id":"https://openalex.org/keywords/hyperbolic-group","display_name":"Hyperbolic group","score":0.491100013256073},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4810999929904938},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.43560001254081726}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9128000140190125},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6245999932289124},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.5896000266075134},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5748000144958496},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5509999990463257},{"id":"https://openalex.org/C167150821","wikidata":"https://www.wikidata.org/wiki/Q81194","display_name":"Hyperbolic group","level":4,"score":0.491100013256073},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4810999929904938},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.43560001254081726},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C131715654","wikidata":"https://www.wikidata.org/wiki/Q288465","display_name":"Group action","level":3,"score":0.2791999876499176},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2531999945640564}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196715500289","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715500289","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"},{"id":"pmh:oai:arXiv.org:1310.4882","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.4882","pdf_url":"https://arxiv.org/pdf/1310.4882","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1310.4882","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.4882","pdf_url":"https://arxiv.org/pdf/1310.4882","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W45735853","https://openalex.org/W176922297","https://openalex.org/W629265671","https://openalex.org/W646383846","https://openalex.org/W1234885875","https://openalex.org/W1606969465","https://openalex.org/W2018996603","https://openalex.org/W2023337331","https://openalex.org/W2031374434","https://openalex.org/W2068638265","https://openalex.org/W2093397547","https://openalex.org/W2315813414","https://openalex.org/W2908335498","https://openalex.org/W4235484205","https://openalex.org/W4240041676","https://openalex.org/W4244441035"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,85,128],"paper":[2,81],"we":[3],"study":[4,29],"group":[5,97],"actions":[6,98],"on":[7,99],"hyperbolic":[8,31,65,100],"\u039b-metric":[9,18,52,66,110],"spaces,":[10],"where":[11],"\u039b":[12],"is":[13],"an":[14,113],"ordered":[15],"abelian":[16],"group.":[17],"spaces":[19,53,67,105,111],"were":[20],"first":[21],"introduced":[22,39],"by":[23],"Morgan":[24],"and":[25,33,87,91,130],"Shalen":[26],"in":[27,127],"their":[28],"of":[30,42,50,63,75,78,96,109],"structures":[32],"then":[34],"Chiswell,":[35],"following":[36],"Gromov's":[37],"ideas,":[38],"the":[40,48,61,76,79,94,102,107,131],"notion":[41],"hyperbolicity":[43],"for":[44,112],"such":[45],"spaces.":[46],"Only":[47],"case":[49,108],"0-hyperbolic":[51],"(that":[54],"is,":[55],"\u039b-trees)":[56],"was":[57,68,82,119],"systematically":[58],"studied,":[59],"while":[60],"theory":[62,95],"general":[64],"not":[69],"developed":[70],"at":[71],"all.":[72],"Hence,":[73],"one":[74],"goals":[77],"present":[80],"to":[83,106,120,133],"fill":[84],"gap":[86],"translate":[88],"basic":[89],"notions":[90],"results":[92],"from":[93],"(in":[101],"usual":[103],"sense)":[104],"arbitrary":[114],"\u039b.":[115],"The":[116],"other":[117],"goal":[118],"show":[121],"some":[122],"principal":[123],"difficulties":[124],"which":[125],"arise":[126],"generalization":[129],"ways":[132],"deal":[134],"with":[135],"them.":[136]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
