  We construct Ionel-Parker's proposed refinement of the standard relative
Gromov-Witten invariants in terms of abelian covers of the symplectic divisor
and discuss in what sense it gives rise to invariants. We use it to obtain some
vanishing results for the standard relative Gromov-Witten invariants. In a
separate paper, we describe to what extent this refinement sharpens the usual
symplectic sum formula and give further qualitative applications.
