Structure of leaves and the complex Kupka-Smale property

Tanya Firsova[1]

  • [1] 5D-148 IMS, Math Tower, Stony Brook University, Stony Brook, NY, USA, 11794-3660

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 5, page 1849-1879
  • ISSN: 0373-0956

Abstract

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We study topology of leaves of 1 -dimensional singular holomorphic foliations of Stein manifolds. We prove that for a generic foliation all leaves, except for at most countably many, are contractible, the rest are topological cylinders. We show that a generic foliation is complex Kupka-Smale.

How to cite

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Firsova, Tanya. "Structure of leaves and the complex Kupka-Smale property." Annales de l’institut Fourier 63.5 (2013): 1849-1879. <http://eudml.org/doc/275508>.

@article{Firsova2013,
abstract = {We study topology of leaves of $1$-dimensional singular holomorphic foliations of Stein manifolds. We prove that for a generic foliation all leaves, except for at most countably many, are contractible, the rest are topological cylinders. We show that a generic foliation is complex Kupka-Smale.},
affiliation = {5D-148 IMS, Math Tower, Stony Brook University, Stony Brook, NY, USA, 11794-3660},
author = {Firsova, Tanya},
journal = {Annales de l’institut Fourier},
keywords = {holomorphic foliations; complex differential equations; Stein manifolds; Kupka-Smale property; generic properties},
language = {eng},
number = {5},
pages = {1849-1879},
publisher = {Association des Annales de l’institut Fourier},
title = {Structure of leaves and the complex Kupka-Smale property},
url = {http://eudml.org/doc/275508},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Firsova, Tanya
TI - Structure of leaves and the complex Kupka-Smale property
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 5
SP - 1849
EP - 1879
AB - We study topology of leaves of $1$-dimensional singular holomorphic foliations of Stein manifolds. We prove that for a generic foliation all leaves, except for at most countably many, are contractible, the rest are topological cylinders. We show that a generic foliation is complex Kupka-Smale.
LA - eng
KW - holomorphic foliations; complex differential equations; Stein manifolds; Kupka-Smale property; generic properties
UR - http://eudml.org/doc/275508
ER -

References

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