Number of minimal components and homologically independent compact leaves for a morse form foliation

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.