Geodesic
Close cohomologous Morse forms with compact leaves
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 515-528 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has a compact leave $\gamma $, then any close cohomologous form has a compact leave close to $\gamma $. Then we prove that the set of Morse forms with compactifiable foliations (foliations with no locally dense leaves) is open in a cohomology class, and the number of homologically independent compact leaves does not decrease under small perturbation of the form; moreover, for generic forms (Morse forms with each singular leaf containing a unique singularity; the set of generic forms is dense in the space of closed 1-forms) this number is locally constant.
We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has a compact leave $\gamma $, then any close cohomologous form has a compact leave close to $\gamma $. Then we prove that the set of Morse forms with compactifiable foliations (foliations with no locally dense leaves) is open in a cohomology class, and the number of homologically independent compact leaves does not decrease under small perturbation of the form; moreover, for generic forms (Morse forms with each singular leaf containing a unique singularity; the set of generic forms is dense in the space of closed 1-forms) this number is locally constant.
DOI : 10.1007/s10587-013-0034-0
Classification : 57R30, 58E05, 58K65
Keywords: Morse form foliation; compact leaf; cohomology class 
@article{10_1007_s10587_013_0034_0,
     author = {Gelbukh, Irina},
     title = {Close cohomologous {Morse} forms with compact leaves},
     journal = {Czechoslovak Mathematical Journal},
     pages = {515--528},
     year = {2013},
     volume = {63},
     number = {2},
     doi = {10.1007/s10587-013-0034-0},
     mrnumber = {3073975},
     zbl = {06236428},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0034-0/}
}
TY  - JOUR
AU  - Gelbukh, Irina
TI  - Close cohomologous Morse forms with compact leaves
JO  - Czechoslovak Mathematical Journal
PY  - 2013
SP  - 515
EP  - 528
VL  - 63
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0034-0/
DO  - 10.1007/s10587-013-0034-0
LA  - en
ID  - 10_1007_s10587_013_0034_0
ER  - 
%0 Journal Article
%A Gelbukh, Irina
%T Close cohomologous Morse forms with compact leaves
%J Czechoslovak Mathematical Journal
%D 2013
%P 515-528
%V 63
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0034-0/
%R 10.1007/s10587-013-0034-0
%G en
%F 10_1007_s10587_013_0034_0
Gelbukh, Irina. Close cohomologous Morse forms with compact leaves. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 515-528. doi: 10.1007/s10587-013-0034-0

Cité par Sources :