| Title:
|
On the structure of a Morse form foliation (English) |
| Author:
|
Gelbukh, I. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
207-220 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The foliation of a Morse form $\omega$ on a closed manifold $M$ is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of $M$ and $\omega$. Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of $\mathop{\rm rk}\omega $ and ${\rm Sing} \omega $. The set of the ranks of all forms defining a given foliation without minimal components is described. It is shown that if $\omega$ has more centers than conic singularities then $b_1(M)=0$ and thus the foliation has no minimal components and homologically non-trivial compact leaves, its folitation graph being a tree. (English) |
| Keyword:
|
number of minimal components |
| Keyword:
|
number of maximal components |
| Keyword:
|
compact leaves |
| Keyword:
|
foliation graph |
| Keyword:
|
rank of a form |
| MSC:
|
57R30 |
| MSC:
|
58K65 |
| idZBL:
|
Zbl 1224.57010 |
| idMR:
|
MR2486626 |
| . |
| Date available:
|
2010-07-20T15:01:51Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140474 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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