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The present paper is a continuation of our earlier work. It explores how the spectral sequence introduced there 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.
We present a new method to prove transversality for holomorphic curves in symplectic manifolds, and show how it leads to a definition of genus zero Gromov-Witten invariants. The main idea is to introduce additional marked points that are mapped to a symplectic hypersurface of high degree in order to stabilize the domains of holomorphic maps.