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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
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Category: math
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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
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Date available: 2010-07-20T15:01:51Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/140474
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