Czechoslovak Mathematical Journal

, Volume 59, Issue 1, pp 207–220 | Cite as

On the structure of a Morse form foliation

  • I. GelbukhEmail author


The foliation of a Morse form ω 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 ω. Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of rk ω and Sing ω. The set of the ranks of all forms defining a given foliation without minimal components is described. It is shown that if ω 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.


number of minimal components number of maximal components compact leaves foliation graph rank of a form 

MSC 2000

57R30 58K65 


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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2009

Authors and Affiliations

  1. 1.CIC-IPNDFMexico

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