# 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

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topFirsova, 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 -

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