{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T09:31:44Z","timestamp":1775208704373,"version":"3.50.1"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"8","license":[{"start":{"date-parts":[[2013,7,1]],"date-time":"2013-07-01T00:00:00Z","timestamp":1372636800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Compositio Math."],"published-print":{"date-parts":[[2013,8]]},"abstract":"Abstract<\/jats:title>\n \n We show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about\n \n \n \n $0\\in \\mathbb{C} $<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is free in the sense of pseudogroups even if the class of conjugacy of the generators is fixed. This result has a number of consequences on the topology\u00a0of leaves for a (singular) holomorphic foliation defined on a neighborhood of an invariant curve. In particular, in the classical and simplest case arising from local nilpotent foliations possessing a unique separatrix which is given by a cusp of the form\n \n \n \n $\\{ {y}^{2} - {x}^{2n+ 1} = 0\\} $<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , our results allow us to settle the problem of showing that a generic foliation possesses only countably many non-simply connected leaves.\n <\/jats:p>","DOI":"10.1112\/s0010437x13007161","type":"journal-article","created":{"date-parts":[[2013,7,1]],"date-time":"2013-07-01T03:55:06Z","timestamp":1372650906000},"page":"1401-1430","source":"Crossref","is-referenced-by-count":3,"title":["Generic pseudogroups on and the topology of leaves"],"prefix":"10.1017","volume":"149","author":[{"given":"J.-F.","family":"Mattei","sequence":"first","affiliation":[]},{"given":"J. C.","family":"Rebelo","sequence":"additional","affiliation":[]},{"given":"H.","family":"Reis","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2013,7,1]]},"reference":[{"key":"S0010437X13007161_r4","doi-asserted-by":"publisher","DOI":"10.5802\/afst.1073"},{"key":"S0010437X13007161_r10","article-title":"Classification analytique des \u00e9quations diff\u00e9rentielles non lin\u00e9aires r\u00e9sonnantes du premier ordre","volume":"16","author":"Martinet","year":"1983","journal-title":"Ann. Sci. \u00c9c. Norm. Sup\u00e9r."},{"key":"S0010437X13007161_r15","first-page":"288","volume-title":"Algebraic and differential topology\u2014global differential geometry","author":"Takens","year":"1984"},{"key":"S0010437X13007161_r14","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.2001.4043"},{"key":"S0010437X13007161_r2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4364-9"},{"key":"S0010437X13007161_r7","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-9593(99)80002-0"},{"key":"S0010437X13007161_r11","doi-asserted-by":"publisher","DOI":"10.24033\/asens.1393"},{"key":"S0010437X13007161_r1","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1996.0163"},{"key":"S0010437X13007161_r6","first-page":"275","article-title":"The monodromy group at infinity of a generic polynomial vector field on the complex projective plane","volume":"2","author":"Il\u2019yashenko","year":"1994","journal-title":"Russ. J. Math. Phys."},{"key":"S0010437X13007161_r9","doi-asserted-by":"publisher","DOI":"10.24033\/asens.2083"},{"key":"S0010437X13007161_r3","doi-asserted-by":"publisher","DOI":"10.1006\/jnth.1997.2202"},{"key":"S0010437X13007161_r5","first-page":"162","article-title":"Topology of analytic foliations in ${ \\mathbb{C} }^{2} $. The Kupka\u2013Smale property","volume":"254","author":"Firsova","year":"2006","journal-title":"Tr. Mat. Inst. Steklova"},{"key":"S0010437X13007161_r16","first-page":"89","article-title":"Centralisateurs et conjugaison diff\u00e9rentiable des diff\u00e9omorphismes du cercle. Petits diviseurs en dimension\u00a01","volume":"231","author":"Yoccoz","year":"1995","journal-title":"Ast\u00e9risque"},{"key":"S0010437X13007161_r13","doi-asserted-by":"crossref","first-page":"415","DOI":"10.17323\/1609-4514-2010-10-2-415-468","article-title":"Relations of formal diffeomorphisms and the center problem","volume":"10","author":"Nakai","year":"2010","journal-title":"Mosc. Math. J."},{"key":"S0010437X13007161_r8","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2006.163.709"},{"key":"S0010437X13007161_r12","unstructured":"[MS04] J.-F. Mattei and E. Salem , Modules formels locaux de feuilletages holomorphes, Preprint (2004), arXiv:math\/0402256v1."}],"container-title":["Compositio Mathematica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0010437X13007161","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T08:35:51Z","timestamp":1775205351000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0010437X13007161\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,1]]},"references-count":16,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2013,8]]}},"alternative-id":["S0010437X13007161"],"URL":"https:\/\/doi.org\/10.1112\/s0010437x13007161","relation":{},"ISSN":["0010-437X","1570-5846"],"issn-type":[{"value":"0010-437X","type":"print"},{"value":"1570-5846","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,1]]}}}