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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability of complex foliations transverse to fibrations


Authors: Fabio Santos and Bruno Scardua
Journal: Proc. Amer. Math. Soc. 140 (2012), 3083-3090
MSC (2010): Primary 37F75, 57R30; Secondary 57R32, 32M05
Published electronically: December 30, 2011
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Abstract: We prove that a holomorphic foliation of codimension $ k$ which is transverse to the fibers of a fibration and has a compact leaf with finite holonomy group is a Seifert fibration, i.e., has all leaves compact with finite holonomy. This is the case for $ C^1$-small deformations of a foliation where the original foliation exhibits a compact leaf and the base $ B$ of the fibration satisfies $ H^1(B,\mathbb{R})=0$ and $ H^1(B, \operatorname {GL}(k,\mathbb{R}))=0$.


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Additional Information

Fabio Santos
Affiliation: Departamento de Geometria, Instituto de Matemática, Universidade Federal Fluminense, Niteroi, Rio de Janeiro 24.020-140, Brazil
Email: fabio@mat.uff.br

Bruno Scardua
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, CP 68530, Rio de Janeiro, RJ, 21945-970, Brazil
Email: scardua@im.ufrj.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11136-5
PII: S 0002-9939(2011)11136-5
Keywords: Foliation, suspension, global holonomy, Seifert fibration.
Received by editor(s): June 6, 2010
Received by editor(s) in revised form: March 19, 2011
Published electronically: December 30, 2011
Communicated by: Brooke Shipley
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.