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Journal Article
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Number of minimal components and homologically independent compact leaves for a morse form foliation
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Authors
Irina Gelbukh 1 
1Moscow State University Department of Mathematics Moscow Russia
2IPN CIC 07738 DF, Mexico Mexico
Abstract
The numbers
m
(
ω
) of minimal components and
c
(
ω
) of homologically independent compact leaves of the foliation of a Morse form
ω
on a connected smooth closed oriented manifold
M
are studied in terms of the first non-commutative Betti number
b
′
1
(
M
). A sharp estimate 0 ≦
m
(
ω
) +
c
(
ω
) ≦
b
′
1
(
M
) is given. It is shown that all values of
m
(
ω
) +
c
(
ω
), and in some cases all combinations of
m
(
ω
) and
c
(
ω
) with this condition, are reached on a given
M
. The corresponding issues are also studied in the classes of generic forms and compactifiable foliations.
Keywords
Primary 57R30, 58K65, Morse form foliation, minimal components, compact leaves
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