On the structure of a Morse form foliation

Gelbukh, I.. "On the structure of a Morse form foliation." Czechoslovak Mathematical Journal 59.1 (2009): 207-220. <http://eudml.org/doc/37918>.

@article{Gelbukh2009,
abstract = {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.},
author = {Gelbukh, I.},
journal = {Czechoslovak Mathematical Journal},
keywords = {number of minimal components; number of maximal components; compact leaves; foliation graph; rank of a form; number of minimal components; number of maximal components; compact leaf; foliation graph; rank of a form},
language = {eng},
number = {1},
pages = {207-220},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the structure of a Morse form foliation},
url = {http://eudml.org/doc/37918},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Gelbukh, I.
TI - On the structure of a Morse form foliation
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 207
EP - 220
AB - 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.
LA - eng
KW - number of minimal components; number of maximal components; compact leaves; foliation graph; rank of a form; number of minimal components; number of maximal components; compact leaf; foliation graph; rank of a form
UR - http://eudml.org/doc/37918
ER -