My question is pretty much as in the title. On page 100 of his thesis, Bourgeois gives a computation of the CZ(or I suppose more correctly this is the Robbin-Salamon index) index of the Reeb orbits and their multiple covers on a prequantization space.

http://tel.archives-ouvertes.fr/docs/00/04/51/90/PDF/tel-00002421.pdf

His method involves constructing some capping of class $\beta_1$ and evaluating the first Chern class on that capping. The same exact computation appears in Eliashberg-Givental and Hofer's paper "Introduction to Symplectic Field Theory"

http://arxiv.org/pdf/math/0010059v1.pdf

in section 2.9.1. The only definition I know of these indices is given very clearly for example at the end of Oancea's paper http://arxiv.org/abs/math/0403377 and seems quite different a priori from what the above authors do. The definition in Oancea's work seems difficult to compute.

The only idea I can think of is that one wants to say that given a holomorphic sphere in the symplectic base $V$ and a choice of point through which the sphere passes, one can lift it to a unique holomorphic cap of the Reeb orbit over $V$, if one chooses a specific complex structure on the total space of the symplectization $\mathbb{R} \times Y$. Then one can get this formula by comparing expected dimensions of moduli spaces. However it is not clear to me whether the complex structure on the total space is sufficiently generic to really make this a rigorous computation.

Presumably, there is a very simple relation between the two definitions since neither author group comments much. How can one link the definition that I mention to the computation that is provided?