The paper under review addresses a general question regarding the possibility to deduce the existence of other closed Reeb orbits from a known set of closed Reeb orbits. For this question, the author presents one approach for a set of closed Reeb orbits with certain knotting or linking properties. In particular, he uses the cylinderical contact homology on Reeb orbit complements and its computations given by Colin and Honda in order to support his approach in certain cases on the 3-sphere.
The paper consists of six sections. In Section 2, some geometric and analytic materials are recalled. Section 3 is devoted to explaining an intersection theory for pseudo-holomorphic curves in symplectizations and deriving some compactness results. Sections 4 describes some necessary chain complexes, maps between them, and so on. In Section 5, one instance with certain knotting or linking properties to give an affirmative answer to the general question, called the implied existence result, is proved. Finally, in Section 6, the author works out some explicit examples on the 3-sphere, in detail.