  We show that on any closed contact manifold of dimension greater than 1 a
contact structure with vanishing contact homology can be constructed. The basic
idea for the construction comes from Giroux. We use a special open book
decomposition for spheres. The page is the cotangent bundle of a sphere and the
monodromy is given by a left-handed Dehn twist. In the resulting contact
manifold we exhibit a closed Reeb orbit that bounds a single finite energy
plane. As a result, the unit element of the contact homology algebra is exact
and so the contact homology vanishes. This result can be extended to other
contact manifolds by using connected sums. The latter is related to the
plumbing- or 2-Murasugi sum of the contact open books. We shall give a possible
description of this construction and some conjectures about the plumbing
operation.
