  In light of recent attempts to extend the Cieliebak-Mohnke approach for
constructing Gromov-Witten invariants to positive genera, we compare the
absolute and relative Gromov-Witten invariants of compact symplectic manifolds
when the symplectic hypersurface contains no relevant holomorphic curves. We
show that these invariants are then the same, except in a narrow range of
dimensions of the target and genera of the domains, and provide examples when
they fail to be the same.
