| Title:
|
Close cohomologous Morse forms with compact leaves (English) |
| Author:
|
Gelbukh, Irina |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
515-528 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Morse form foliation |
| Keyword:
|
compact leaf |
| Keyword:
|
cohomology class |
| MSC:
|
57R30 |
| MSC:
|
58E05 |
| MSC:
|
58K65 |
| idZBL:
|
Zbl 06236428 |
| idMR:
|
MR3073975 |
| DOI:
|
10.1007/s10587-013-0034-0 |
| . |
| Date available:
|
2013-07-18T15:06:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143329 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
