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What is an example of a codimension one foliation of a manifold for which this cohomology is finite dimension for all dimension $*$?

Moreover what is the description of this cohomology for the Reeb foliation of $S^{3}$?

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    $\begingroup$ $H^1$ is never finite dimensional: it contains at least $\Omega^0\wedge\alpha$. $\endgroup$ Jan 30, 2015 at 20:18
  • $\begingroup$ @AlexDegtyarev Thank you. So what about if we restrict ourselves to even cohomology? $\endgroup$ Jan 30, 2015 at 20:24

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