{"id":"https://openalex.org/W1925983623","doi":"https://doi.org/10.1112/jlms/jdu069","title":"Cannon-Thurston fibers for iwip automorphisms of FN","display_name":"Cannon-Thurston fibers for iwip automorphisms of FN","publication_year":2015,"publication_date":"2015-01-16","ids":{"openalex":"https://openalex.org/W1925983623","doi":"https://doi.org/10.1112/jlms/jdu069","mag":"1925983623"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdu069","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu069","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1207.3494","any_repository_has_fulltext":true},"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":["Department of Mathematics, University of Illinois at Urbana\u2010Champaign, 1409 West Green Street, Urbana, IL 61801, USA, kapovich@math.uiuc.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois at Urbana\u2010Champaign, 1409 West Green Street, Urbana, IL 61801, USA, kapovich@math.uiuc.edu","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081959625","display_name":"Martin Lustig","orcid":null},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Martin Lustig","raw_affiliation_strings":["LATP, Centre de Math\u00e9matiques et InformatiqueAix-Marseille Universit\u00e939, rue F. Joliot Curie13453 Marseille 13France"],"affiliations":[{"raw_affiliation_string":"LATP, Centre de Math\u00e9matiques et InformatiqueAix-Marseille Universit\u00e939, rue F. Joliot Curie13453 Marseille 13France","institution_ids":["https://openalex.org/I4210138206","https://openalex.org/I21491767"]}]}],"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":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":2.7043,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.88503357,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"91","issue":"1","first_page":"203","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9987999796867371,"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/T11567","display_name":"semigroups and automata theory","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.8018405437469482},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6996968388557434},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6700432300567627},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.6459792256355286},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.48166000843048096},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.4663744568824768}],"concepts":[{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.8018405437469482},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6996968388557434},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6700432300567627},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6459792256355286},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.48166000843048096},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.4663744568824768},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1112/jlms/jdu069","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu069","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1207.3494","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1207.3494","pdf_url":"https://arxiv.org/pdf/1207.3494","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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01318434v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01318434","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of the London Mathematical Society, 2015, 91 (1), pp.203--224. ⟨10.1112/jlms/jdu069⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1207.3494","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1207.3494","pdf_url":"https://arxiv.org/pdf/1207.3494","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W28957298","https://openalex.org/W54401119","https://openalex.org/W126237762","https://openalex.org/W1483877865","https://openalex.org/W1493096988","https://openalex.org/W1541534581","https://openalex.org/W1570194207","https://openalex.org/W1571539704","https://openalex.org/W1637103319","https://openalex.org/W1678471064","https://openalex.org/W1753720811","https://openalex.org/W1826076888","https://openalex.org/W1967057555","https://openalex.org/W1971745120","https://openalex.org/W1972545445","https://openalex.org/W1984093256","https://openalex.org/W1984432802","https://openalex.org/W1990796335","https://openalex.org/W1993482570","https://openalex.org/W1998022780","https://openalex.org/W2001210194","https://openalex.org/W2004924708","https://openalex.org/W2004967419","https://openalex.org/W2014840243","https://openalex.org/W2023444814","https://openalex.org/W2033475234","https://openalex.org/W2034592120","https://openalex.org/W2042420419","https://openalex.org/W2054829256","https://openalex.org/W2064521394","https://openalex.org/W2065123881","https://openalex.org/W2066394251","https://openalex.org/W2083803872","https://openalex.org/W2089644649","https://openalex.org/W2093177117","https://openalex.org/W2095100353","https://openalex.org/W2113344217","https://openalex.org/W2117261597","https://openalex.org/W2126877453","https://openalex.org/W2136649217","https://openalex.org/W2153586689","https://openalex.org/W2160742274","https://openalex.org/W2164754957","https://openalex.org/W2165455462","https://openalex.org/W2167566947","https://openalex.org/W2283605069","https://openalex.org/W2289523244","https://openalex.org/W2318910871","https://openalex.org/W2512542594","https://openalex.org/W2964313702","https://openalex.org/W2998763814","https://openalex.org/W3100402813","https://openalex.org/W3102087734","https://openalex.org/W3102730101","https://openalex.org/W3103006240","https://openalex.org/W3104346305","https://openalex.org/W3122849838","https://openalex.org/W6601135287","https://openalex.org/W6637564220","https://openalex.org/W6684267927"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3015672237","https://openalex.org/W1607139407","https://openalex.org/W4256653909","https://openalex.org/W2911989606","https://openalex.org/W1972989769","https://openalex.org/W2068180495","https://openalex.org/W3026958673","https://openalex.org/W3140259146","https://openalex.org/W2064732611"],"abstract_inverted_index":{"For":[0],"any":[1,38],"atoroidal":[2],"iwip":[3],"$\\\\phi":[4],"\\\\in":[5],"Out(F_N)$":[6],"the":[7,15,42,49,76,100],"mapping":[8],"torus":[9],"group\\n$G_\\\\phi=F_N\\\\rtimes_\\\\phi":[10],"<t>e$":[11],"is":[12,46],"hyperbolic,":[13],"and":[14],"embedding":[16],"$\\\\iota:":[17],"F_N\\n\\\\overset{\\\\lhd}{\\\\longrightarrow}":[18],"G_\\\\phi$":[19,56,68,98,120],"induces":[20],"a":[21],"continuous,":[22],"$F_N$-equivariant\\nand":[23],"surjective":[24],"{\\\\em":[25,94],"Cannon-Thurston":[26],"map}":[27],"$\\\\hat":[28,44],"\\\\iota:":[29],"\\\\partial":[30,67],"F_N":[31],"\\\\to":[32],"\\\\partial\\nG_\\\\phi$.\\n":[33],"We":[34,60],"prove":[35,62],"that":[36,48,63,111],"for":[37,112],"$\\\\phi$":[39],"as":[40],"above,":[41],"map":[43],"\\\\iota$":[45],"finite-to-one\\nand":[47],"preimage":[50],"of":[51,54,92,103,126],"every":[52,64],"point":[53,65],"$\\\\partial":[55,73,97,133],"has":[57,75],"cardinality":[58],"$\\\\le\\n2N$.\\n":[59],"also":[61],"$S\\\\in":[66],"with":[69],"$\\\\ge":[70],"3$":[71],"preimages\\nin":[72],"F_N$":[74],"form":[77],"$(wt^m)^\\\\infty$":[78],"where":[79],"$w\\\\in":[80],"F_N,":[81],"m\\\\ne":[82],"0$,":[83],"and\\nthat":[84],"there":[85,114],"are":[86,115],"at":[87],"most":[88],"$4N-5$":[89],"distinct":[90],"$F_N$-orbits":[91,125],"such":[93,127],"singular}\\npoints":[95],"in":[96,132],"(for":[99],"translation":[101],"action":[102],"$F_N$":[104],"on":[105],"$\\\\partial\\nG_\\\\phi$).\\n":[106],"By":[107],"contrast,":[108],"we":[109],"show":[110],"$k=1,2$":[113],"uncountably":[116,123],"many":[117,124],"points":[118],"$S\\\\in\\n\\\\partial":[119],"(and":[121],"thus":[122],"$S$)":[128],"with\\nexactly":[129],"$k$":[130],"preimages":[131],"F_N$.\\n":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}