{"id":"https://openalex.org/W1989911299","doi":"https://doi.org/10.1515/crelle.2009.001","title":"The holonomy groupoid of a singular foliation","display_name":"The holonomy groupoid of a singular foliation","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1989911299","doi":"https://doi.org/10.1515/crelle.2009.001","mag":"1989911299"},"language":"de","primary_location":{"id":"doi:10.1515/crelle.2009.001","doi":"https://doi.org/10.1515/crelle.2009.001","is_oa":false,"landing_page_url":"https://doi.org/10.1515/crelle.2009.001","pdf_url":null,"source":{"id":"https://openalex.org/S62223294","display_name":"Journal f\u00fcr die reine und angewandte Mathematik (Crelles Journal)","issn_l":"0075-4102","issn":["0075-4102","1435-5345"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal f\u00fcr die reine und angewandte Mathematik (Crelles Journal)","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.zora.uzh.ch/id/eprint/23589/1/0612370v4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076388853","display_name":"Iakovos Androulidakis","orcid":"https://orcid.org/0000-0001-9171-6650","observed_orcids":["https://orcid.org/0000-0001-9171-6650"]},"institutions":[{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Iakovos Androulidakis","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universit\u00e4t Z\u00fcrich, Winterthurerstrasse 190, 8057 Z\u00fcrich, Schweiz. e-mail: iakovos.androulidakis@math.unizh.ch","[University of Zurich, Z\u00fcrich, Switzerland]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Z\u00fcrich, Winterthurerstrasse 190, 8057 Z\u00fcrich, Schweiz. e-mail: iakovos.androulidakis@math.unizh.ch","institution_ids":["https://openalex.org/I202697423"]},{"raw_affiliation_string":"[University of Zurich, Z\u00fcrich, Switzerland]","institution_ids":["https://openalex.org/I202697423"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108227055","display_name":"Georges Skandalis","orcid":"https://orcid.org/0000-0003-2174-145X","observed_orcids":["https://orcid.org/0000-0003-2174-145X"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I4387154366","display_name":"Universit\u00e9 Paris Diderot","ror":"https://ror.org/02n7qrg46","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241","https://openalex.org/I4387154366"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Georges Skandalis","raw_affiliation_strings":["Institut de Math\u00e9matiques de Jussieu, UMR 7586, CNRS\u2014Universit\u00e9 Diderot\u2014Paris 7, 175, rue du Chevaleret, 75013 Paris, France. e-mail: skandal@math.jussieu.fr","Universit\u00e9 Paris 7 \u2013 Denis-Diderot, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu, UMR 7586, CNRS\u2014Universit\u00e9 Diderot\u2014Paris 7, 175, rue du Chevaleret, 75013 Paris, France. e-mail: skandal@math.jussieu.fr","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I3017942884"]},{"raw_affiliation_string":"Universit\u00e9 Paris 7 \u2013 Denis-Diderot, Paris, France","institution_ids":["https://openalex.org/I4387154366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2400,"currency":"EUR","value_usd":2712},"apc_paid":null,"fwci":2.5647,"has_fulltext":true,"cited_by_count":134,"citation_normalized_percentile":{"value":0.87122908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":"2009","issue":"626","first_page":"1","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.4097000062465668,"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"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.4097000062465668,"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":0.21610000729560852,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.13830000162124634,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/holonomy-groupoid","display_name":"holonomy groupoid","score":0.9819999933242798},{"id":"https://openalex.org/keywords/singular-foliations","display_name":"singular foliations","score":1.0},{"id":"https://openalex.org/keywords/analytic-index","display_name":"analytic index","score":0.8230000138282776},{"id":"https://openalex.org/keywords/k-theory","display_name":"K-theory","score":0.7829999923706055}],"concepts":[{"id":"https://openalex.org/C75328951","wikidata":"https://www.wikidata.org/wiki/Q17008126","display_name":"Double groupoid","level":2,"score":0.9130734801292419},{"id":"https://openalex.org/C32518243","wikidata":"https://www.wikidata.org/wiki/Q907926","display_name":"Holonomy","level":2,"score":0.8770682215690613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.782660186290741},{"id":"https://openalex.org/C168425004","wikidata":"https://www.wikidata.org/wiki/Q525802","display_name":"Foliation (geology)","level":3,"score":0.7795916795730591},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.577918529510498},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5738295316696167},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46076300740242004},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.12177371978759766},{"id":"https://openalex.org/C17409809","wikidata":"https://www.wikidata.org/wiki/Q161764","display_name":"Geochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C26687426","wikidata":"https://www.wikidata.org/wiki/Q47069","display_name":"Metamorphic rock","level":2,"score":0.0}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.1515/crelle.2009.001","doi":"https://doi.org/10.1515/crelle.2009.001","is_oa":false,"landing_page_url":"https://doi.org/10.1515/crelle.2009.001","pdf_url":null,"source":{"id":"https://openalex.org/S62223294","display_name":"Journal f\u00fcr die reine und angewandte Mathematik (Crelles Journal)","issn_l":"0075-4102","issn":["0075-4102","1435-5345"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal f\u00fcr die reine und angewandte Mathematik (Crelles Journal)","raw_type":"journal-article"},{"id":"pmh:oai:www.zora.uzh.ch:23589","doi":null,"is_oa":true,"landing_page_url":"https://www.zora.uzh.ch/id/eprint/23589/1/0612370v4.pdf","pdf_url":"https://www.zora.uzh.ch/id/eprint/23589/1/0612370v4.pdf","source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Androulidakis, I; Skandalis, G (2009). The holonomy groupoid of a singular foliation. Journal f\u00fcr die Reine und Angewandte Mathematik, 626:1-37.","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:math/0612370","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0612370","pdf_url":"https://arxiv.org/pdf/math/0612370","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"pmh:oai:doc.rero.ch:296182","doi":null,"is_oa":false,"landing_page_url":"http://doc.rero.ch/record/296182/files/crelle.2009.001.pdf","pdf_url":"http://doc.rero.ch/record/296182/files/crelle.2009.001.pdf","source":{"id":"https://openalex.org/S4306400148","display_name":"reroDoc Digital Library","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.3611","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.3611","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/math/0612370v4.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.361.8651","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.361.8651","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uzh.ch/fileadmin/math/preprints/AS0412.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.923.5276","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.923.5276","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uoc.gr/%7Eiakovos/IA/Iakovos_Androulidakis_files/HolGpd_Crelle.pdf","raw_type":"text"},{"id":"pmh:oai:www.zora.uzh.ch:20.500.14742/45261","doi":null,"is_oa":true,"landing_page_url":"https://www.zora.uzh.ch/handle/20.500.14742/45261","pdf_url":null,"source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Androulidakis, I., & Skandalis, G. (2009). The holonomy groupoid of a singular foliation. Journal F\u00fcr Die Reine Und Angewandte Mathematik, 626, 1\u201337. https://doi.org/10.1515/CRELLE.2009.001","raw_type":"Journal Article"},{"id":"doi:10.48550/arxiv.math/0612370","doi":"https://doi.org/10.48550/arxiv.math/0612370","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math/0612370","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5167/uzh-23589","doi":"https://doi.org/10.5167/uzh-23589","is_oa":true,"landing_page_url":"https://doi.org/10.5167/uzh-23589","pdf_url":null,"source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:www.zora.uzh.ch:23589","doi":null,"is_oa":true,"landing_page_url":"https://www.zora.uzh.ch/id/eprint/23589/1/0612370v4.pdf","pdf_url":"https://www.zora.uzh.ch/id/eprint/23589/1/0612370v4.pdf","source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Androulidakis, I; Skandalis, G (2009). The holonomy groupoid of a singular foliation. Journal f\u00fcr die Reine und Angewandte Mathematik, 626:1-37.","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323874","display_name":"Universit\u00e4t Z\u00fcrich","ror":"https://ror.org/02crff812"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1989911299.pdf","grobid_xml":"https://content.openalex.org/works/W1989911299.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W2526473","https://openalex.org/W1533163381","https://openalex.org/W1539551388","https://openalex.org/W1585629377","https://openalex.org/W1820959250","https://openalex.org/W1842821338","https://openalex.org/W1988724155","https://openalex.org/W1995892714","https://openalex.org/W2005965240","https://openalex.org/W2011621741","https://openalex.org/W2017994258","https://openalex.org/W2018595627","https://openalex.org/W2023825378","https://openalex.org/W2027992356","https://openalex.org/W2037137741","https://openalex.org/W2081438312","https://openalex.org/W2104487022","https://openalex.org/W2146090462","https://openalex.org/W2152887332","https://openalex.org/W2170256719","https://openalex.org/W2963047161","https://openalex.org/W2963824957","https://openalex.org/W3120063418"],"related_works":["https://openalex.org/W7095769978","https://openalex.org/W3110100582","https://openalex.org/W2084884538","https://openalex.org/W7134862840","https://openalex.org/W6992581136","https://openalex.org/W2992984403","https://openalex.org/W4409867039","https://openalex.org/W2313870107","https://openalex.org/W3022788973","https://openalex.org/W2995420508"],"abstract_inverted_index":{"We":[0,182],"construct":[1],"the":[2,10,17,41,45,56,136,139,151,170,176,180,185,192,203,213,223,231,236],"holonomy":[3,19,140],"groupoid":[4,14,20,141,166,229,234],"of":[5,21,30,48,59,97,112,125,130,175,179,187,195,206,218,225,238,240],"any":[6],"singular":[7,46,61,113,171],"foliation.":[8,181,232],"In":[9,135,210],"regular":[11],"case":[12,172],"this":[13,165],"coincides":[15],"with":[16,243],"usual":[18],"Winkelnkemper":[22,26],"([":[23],"H.":[24],"E.":[25],",":[27,52,77,94,109],"The":[28],"graph":[29,58],"a":[31,60,157,188,196,219,226],"foliation,":[32,62],"Ann.":[33],"Glob.":[34],"Anal.":[35],"Geom.":[36,65,117],"1":[37],"(3)":[38],"(1983),":[39],"51\u201375.]);":[40],"same":[42],"holds":[43],"in":[44,202],"cases":[47],"[":[49,72,91,106],"J.":[50,75,115],"Pradines":[51,76],"How":[53],"to":[54,167,169,245],"define":[55],"differentiable":[57],"C.":[63,82,92,107],"Top.":[64],"Diff.":[66,116],"Cat.":[67],"XXVI":[68],"(4)":[69],"(1985),":[70,89],"339\u2013381.],":[71],"B.":[73],"Bigonnet,":[74],"Graphe":[78],"d'un":[79],"feuilletage":[80],"singulier,":[81],"R.":[83],"Acad.":[84],"Sci.":[85],"Paris":[86],"300":[87],"(13)":[88],"439\u2013442.],":[90],"Debord":[93,108],"Local":[95],"integration":[96],"Lie":[98,228],"algebroids,":[99],"Banach":[100],"Center":[101],"Publ.":[102],"54":[103],"(2001),":[104,119],"21\u201333.],":[105],"Holonomy":[110],"groupoids":[111],"foliations,":[114],"58":[118],"467\u2013500.],":[120],"which":[121,221],"from":[122],"our":[123,207,211],"point":[124],"view":[126],"can":[127,142],"be":[128,143],"thought":[129],"as":[131],"being":[132],"\u201calmost":[133],"regular\u201d.":[134],"general":[137],"case,":[138],"quite":[144],"an":[145,246],"ill":[146],"behaved":[147],"geometric":[148],"object.":[149],"On":[150],"other":[152],"hand":[153],"it":[154],"often":[155],"has":[156],"nice":[158],"longitudinal":[159,189],"smooth":[160],"structure.":[161],"Nonetheless,":[162],"we":[163],"use":[164],"generalize":[168],"Connes'":[173],"construction":[174,186],"C":[177,208],"*-algebra":[178],"also":[183],"outline":[184],"pseudo-differential":[190],"calculus;":[191],"analytic":[193],"index":[194],"longitudinally":[197],"elliptic":[198],"operator":[199],"takes":[200],"place":[201],"K":[204],"-theory":[205],"*-algebra.":[209],"construction,":[212],"key":[214],"notion":[215],"is":[216,235],"that":[217],"bi-submersion":[220],"plays":[222],"role":[224],"local":[227],"defining":[230],"Our":[233],"quotient":[237],"germs":[239],"these":[241],"bi-submersions":[242],"respect":[244],"appropriate":[247],"equivalence":[248],"relation.":[249]},"counts_by_year":[{"year":2026,"cited_by_count":15},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2016-06-24T00:00:00"}
