  The present paper explores how the spectral sequence introduced in a previous
work (and obtained by taking moduli spaces of any dimension into account in the
Floer construction), interacts with the presence of bubbling. As consequences
are obtained some relations between binary Gromov-Witten invariants and
relative Ganea-Hopf invariants, a criterion for detecting the monodromy of
bubbling as well as algebraic criteria for the detection of periodic orbits.
