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Topology and characteristic closures of K-contact
manifolds

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*Philippe Rukimbira*

**E-mail:** rukim@fiu.edu
**Abstract.** The dimension of a characteristic closure on a closed
K-contact 2n+1-manifold $M$ is at most the smaller of n+1 and 2n+1 minus
the rank of the vector space of harmonic vector fields on $M$. Moreover,
there are at least n+1 closed characteristics on $M$ and if their number
is finite, then each of the Betti numbers of $M$ is at most equal to 1.
If in addition, $M$ is simply connected, then it is homeomorphic to a sphere.

**AMSclassification.** Primary 58F22, 58F18; Secondary 53C15

**Keywords.** K-contact, Betti number, Morse Theory