Just wanted to know if Giroux's theorem for 3-dimensional contact manifolds can be generalized:

In contact geometry for manifolds of dimension 3 , we have Giroux's theorem , stating that for any compact, oriented manifold there is a bijection between the set of contact structures up to isotopy and the set of open book decomposition up to the operation of positive stabilization (meaning that any two stabilized manifolds give rise under Giroux's theorem, to the same contact structure up to isotopy). Open books are known to exist for all odd-dimensional manifolds.

Are there similar relationships on (2n+1)-manifolds, n>1 say compact and oriented, between contact structures and open books, or between open books and some other property?

Thanks.