Cylindrical contact homology of 3-dimensional Brieskorn manifolds

Cylindrical contact homology is a comparatively simple incarnation of symplectic field theory whose existence and invariance under suitable hypotheses was recently established by Hutchings and Nelson. We study this invariant for a general Brieskorn 3-manifold $\mathrm{\Sigma }(a_1,\dots ,a_n)$, and give a complete description of the cylindrical contact homology for this 3-manifold equipped with its natural contact structure, for any $a_j$ satisfying $\frac{1}{a_1}+\cdots +\frac{1}{a_n}<n-2$.