Cylindrical contact homology of 3-dimensional Brieskorn manifolds

Cylindrical contact homology for contact 3-manifolds is a comparatively simple incarnation of symplectic field theory whose existence and invariance under suitable hypotheses was recently established by Hutchings and Nelson (and, in a slightly different form, by Bao and Honda). We study this invariant for a general Brieskorn 3-manifold Sigma(a(1),....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 1/a(1) +...+1/a(n) < n - 2.